Answer:
Step-by-step explanation:
Hello!
To test the claim that eating a healthy breakfast improves the performance of students on their test a math teacher randomly asked 46 students what did they have for breakfast before they took the final exam and classified them as:
Group 1: Ate healthy breakfast
X₁: Number of students that ate a healthy breakfast before the exam and earned 80% or higher.
n₁= 26
Group 2: Did not eat healthy breakfast
X₂: Number of students that did not eat a healthy breakfast before the exam and earned 80% or higher.
n₂= 20
After the test she counted the number of students that got 80% or more in the test for each group obtaining the following sample proportions:
p'₁= 0.50
p'₂= 0.40
The parameters of study are the population proportions, if the claim is true then p₁ > p₂
And you can determine the hypotheses as
H₀: p₁ ≤ p₂
H₁: p₁ > p₂
α: 0.05
[tex]Z= \frac{(p'_1-p'_2)-(p_1-p_2)}{\sqrt{p'(1-p')[\frac{1}{n_1} +\frac{1}{n_2}] } } }[/tex]≈N(0;1)
pooled sample proportion: [tex]p'= \frac{x_1+x_2}{n_1+n_2} =\frac{13+8}{46} = 0.46[/tex]
[tex]Z_{H_0}= \frac{(0.5-0.4)-0}{\sqrt{0.46(1-0.46)[\frac{1}{26} +\frac{1}{20}] } } }= 0.67[/tex]
p-value: 0.2514
The decision rule is:
If p-value ≤ α, reject the null hypothesis.
If p-value > α, do not reject the null hypothesis.
The p-value: 0.2514 is greater than the significance level 0.05, the test is not significant.
At a 5% significance level you can conclude that the population proportion of math students that obtained at least 80% in the test and had a healthy breakfast is equal or less than the population proportion of math students that obtained at least 80% in the test and didn't have a healthy breakfast.
So having a healthy breakfast doesn't seem to improve the grades of students.
I hope this helps!
The weight of oranges growing in an orchard is normally distributed with a mean weight of 6 oz. and a standard deviation of 0.5 oz. Using the empirical rule, determine what interval would represent weights of the middle 95% of all oranges from this orchard.
Answer:
The interval that would represent weights of the middle 95% of all oranges from this orchard is from 5 oz to 7 oz.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 6
Standard deviation = 0.5
Middle 95% of weights:
By the Empirical Rule, within 2 standard deviations of the mean.
6 - 2*0.5 = 5
6 + 2*0.5 = 7
The interval that would represent weights of the middle 95% of all oranges from this orchard is from 5 oz to 7 oz.
The interval representing the weights of the middle 95% of all oranges from this orchard is from 5 oz to 7 oz.
The Empirical Rule states that for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
What is the empirical rule?The empirical rule says that, in a standard data set, virtually every piece of data will fall within three standard deviations of the mean.
95% of the measures are within 2 standard deviations of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 6
Standard deviation = 0.5
Middle 95% of weights
By the Empirical Rule, within 2 standard deviations of the mean.
6 - 2*0.5 = 5
6 + 2*0.5 = 7
The interval representing the weights of the middle 95% of all oranges from this orchard is from 5 oz to 7 oz.
To learn more about the empirical rule visit:
https://brainly.com/question/24244232
#SPJ5
Which statement accurately describes chemical rocks?
Answer:
Chemical rocks form when minerals dissolve in a solution and crystalize.
Answer:
Chemical rocks don't form from solidification from a melt
Step-by-step explanation:
Given the functions f(x) = 6x + 11 and g(x) = x^2 + 6, which of the following functions represents f[g(x)] correctly?
Answer:
Solve -x2+11xandg+6x-6 = 0
Step-by-step explanation:
If a person is randomly selected, find the probability that his or her birthday is not on New Year's Day. Ignore leap years.
Answer:
Ignoring leap years, May has 31 days, a year has 365 days. 334 days of the year are NOT in May so the probability of a birthday not being in May = 334/365 = approximately 91.5%
Step-by-step explanation:
The probability of event A which represents that the man's birthday is not on New Year's Day is 0.99.
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur. Mathematically -
P(A) = n(A)/n(S)
Given is a person who is randomly selected.
Assume that Event A represents that the man's birthday is not on New Year's Day.
Total number of days in a year = n(S) = 365
Total number of days not on New Year's Day = n(A) = 364
Therefore, the probability that the man's birthday is in May will be -
P(A) = n(A)/n(S)
P(A) = 364/365
P(A) = 0.99
Therefore, the probability of event A which represents that the man's birthday is not on New Year's Day is 0.99.
To solve more questions on Probability, visit the link below-
brainly.com/question/4167983
#SPJ4
Use slopes and y-intercepts to determine if the lines y=5x+5 and 5x−y=−5 are parallel.
Answer: They are not parallel, they are coincident
Step-by-step explanation:
If two lines have the same slope but a different y-intercept, the lines are parallel. If two lines have the same slope and the same y-intercept, the lines are coincident.
We can rewrite 5x−y=−5 adding -5x to both sides and multiplying by -1:
5x - y =-5
5x - y -5x = -5 - 5x (adding -5x to both sides)
-y = -5 - 5x
Multiplying by -1
y = 5x + 5
Both equations look the same so they are coincident. They have the same intercept y=5 and the same slope m=5.
Suppose that x has a binomial distribution with n = 201 and p = 0.45. (Round np and n(1-p) answers to 2 decimal places. Round your answers to 4 decimal places. Round z values to 2 decimal places. Round the intermediate value (σ) to 4 decimal places.) (a) Show that the normal approximation to the binomial can appropriately be used to calculate probabilities about x.
Answer:
a) It can be used because np and n(1-p) are both greater than 5.
Step-by-step explanation:
Binomial distribution and approximation to the normal:
The binomial distribution has two parameters:
n, which is the number of trials.
p, which is the probability of a success on a single trial.
If np and n(1-p) are both greater than 5, the normal approximation to the binomial can appropriately be used.
In this question:
[tex]n = 201, p = 0.45[/tex]
So, lets verify the conditions:
np = 201*0.45 = 90.45 > 5
n(1-p) = 201*(1-0.45) = 201*0.55 = 110.55 > 5
Since both np and n(1-p) are greater than 5, the approximation can be used.
A nurse’s aide earns $375 per week for 50 weeks of the year. What are her total earnings for the year?
Answer:
$18,750
Step-by-step explanation:
Take the earnings per week times the number of weeks
50 * 375
18,750
Answer:
$18,750
Step-by-step explanation:
If we want to find the nurse's aide's earnings for the year, we have to multiply her weekly salary by the number of weeks she worked.
weekly salary * number of weeks
She earns $375 per week and she worked for 50 weeks.
$375*50 weeks
375*50
Multiply the 2 numbers
18,750
Her total earnings for the year are $18,750
A cereal box is an example of a____ a0___ a1.
Answer:
rectangular prism
Step-by-step explanation:
A rectangular prism has 6 sides that are rectangles.
Solve the system of equations by finding the reduced row-echelon form of the augmented matrix for the system of equations.
2x + y + 4z = 16
5x - 2y + 2z = -1
X + 2y - 32 = -9
a. (-1, 2, 22)
c. (-1, 2, 4)
b. (-10, 22, 42)
d. (-10, 2, 22)
The solution to the system of equations is (-1, 2, 4), which is equal to choice (c) (-1, 2, 4).
What is the system of equations?One or many equations having the same number of unknowns that can be solved simultaneously are called simultaneous equations. And the simultaneous equation is the system of equations.
To solve the system of equations, we can represent it in an augmented matrix and use row operations to find its reduced row-echelon form.
The augmented matrix for the system is:
[ 2 1 4 | 16 ]
[ 5 -2 2 | -1 ]
[ 1 2 -3 | -9 ]
We want to get the matrix in reduced row-echelon form.
We can start by using row operations to get a 1 in the upper left corner:
R(1/2) -> R1:
[ 1 1/2 2 | 8 ]
[ 5 -2 2 | -1 ]
[ 1 2 -3 | -9 ]
Now we want to get zeros in the first column below the pivot element (1). We can do this by subtracting 5 times the first row from the second row, and subtracting the first row from the third row:
-5R1 + R2 -> R2:
-R1 + R3 -> R3:
[ 1 1/2 2 | 8 ]
[ 0 -9/2 -8 | -41 ]
[ 0 3/2 -5 | -17 ]
R2 + R3 -> R3:
[ 1 1/2 2 | 8 ]
[ 0 -9/2 -8 | -41 ]
[ 0 -3 -13 | -58 ]
We can continue with row operations to get a 1 in the second row, second column:
(-2/9)R2 -> R2:
[ 1 1/2 2 | 8 ]
[ 0 1 16/9 | 82/9 ]
[ 0 -3 -13 | -58 ]
3R2 + R3 -> R3:
[ 1 1/2 2 | 8 ]
[ 0 1 16/9 | 82/9 ]
[ 0 0 -23/3 | -92/3 ]
Finally, we can get a 1 in the third row, third column:
(-3/23)R3 -> R3:
[ 1 1/2 2 | 8 ]
[ 0 1 16/9 | 82/9 ]
[ 0 0 1 | 4 ]
Now the matrix is in reduced row-echelon form.
We can read the solution directly from the last column:
x = 8 - (1 + 8) = -1
y = 82/9 - (16/9)(4) = 2
z = 4
Therefore, the solution to the system of equations is (-1, 2, 4).
To learn more about the system of equations;
brainly.com/question/13729904
#SPJ7
Budget
8.) If Peter Gower paid $650 for rent
monthly for an entirely year, how
much should he budget for rent
each month?
Answer:
I
(a) $108.33
(b) $54.17
(c) $7.800
(d) $650
Suppose 221 subjects are treated with a drug that is used to treat pain and 51 of them developed nausea. Use a 0.10 significance level to test the claim that more than 20% of users develop nausea.
Answer:
[tex]z=\frac{0.231 -0.2}{\sqrt{\frac{0.2(1-0.2)}{221}}}=1.152[/tex]
The p avlue for this case is given by:
[tex]p_v =P(z>1.152)=0.125[/tex]
The p value for this case is higher than the significance level so then we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true proportion is higher than 0.2 or 20%
Step-by-step explanation:
Information provided
n=221 represent the random sample taken
X=51 represent the people with nausea
[tex]\hat p=\frac{51}{221}=0.231[/tex] estimated proportion of people with nausea
[tex]p_o=0.21[/tex] is the value to test
[tex]\alpha=0.1[/tex] represent the significance level
z would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to verify
We want to check if the true population is higher than 0.20, the system of hypothesis are.:
Null hypothesis:[tex]p \leq 0.2[/tex]
Alternative hypothesis:[tex]p > 0.2[/tex]
The statistic is given:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info given we got:
[tex]z=\frac{0.231 -0.2}{\sqrt{\frac{0.2(1-0.2)}{221}}}=1.152[/tex]
The p avlue for this case is given by:
[tex]p_v =P(z>1.152)=0.125[/tex]
The p value for this case is higher than the significance level so then we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true proportion is higher than 0.2 or 20%
If A = (0, 0) and B = (6, 3) what is the length of overline AB ?
Answer:
A= (0,0) and B = (6,3)
We can find the length AB with the following formula:
[tex] d = \sqrt{(x_B -x_A)^2 +(y_B -y_A)^2}[/tex]
And replacing we got:
[tex] d = \sqrt{(6-0)^2 +(3-0)^2} = \sqrt{45}= 3\sqrt{5}[/tex]
So then the length AB would be [tex] 3\sqrt{5}[/tex]
Step-by-step explanation:
For this case we have the following two points:
A= (0,0) and B = (6,3)
We can find the length AB with the following formula:
[tex] d = \sqrt{(x_B -x_A)^2 +(y_B -y_A)^2}[/tex]
And replacing we got:
[tex] d = \sqrt{(6-0)^2 +(3-0)^2} = \sqrt{45}= 3\sqrt{5}[/tex]
So then the length AB would be [tex] 3\sqrt{5}[/tex]
Answer:6.71
Step-by-step explanation: awesomeness
Salid bought 30 feet of window trim at a hardware store. The trim cost $1.75 per foot including sales tax. If Salid paid with a $100.00 bill, how much change should he have received?
Answer:
47.50
Step-by-step explanation:
According to the question above Salid bought 30 feet of window at a hardware trim store
The trim cost of each window is $1.75 per foot with an inclusion of sales tax added to this amount
= $1.75×30
= 52.5
Since Salid paid for the trim service with a cash of $100.00, his change is calculated as follows
=$100-52.5
= $47.50
Hence Salid change is $47.50
which interval describes the range of this function?
Answer:
Range. The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain. In plain English, the definition means: The range is the resulting y-values we get after substituting all the possible x-values
Step-by-step explanation:
Determine the maximized area of a rectangle that has a perimeter equal to 56m by creating and solving a quadratic equation. What is the length and width?
Answer:
Area of rectangle = [tex]196\,m^2[/tex]
Length of rectangle = 14 m
Width of rectangle = 14 m
Step-by-step explanation:
Given:
Perimeter of rectangle is 56 m
To find: the maximized area of a rectangle and the length and width
Solution:
A function [tex]y=f(x)[/tex] has a point of maxima at [tex]x=x_0[/tex] if [tex]f''(x_0)<0[/tex]
Let x, y denotes length and width of the rectangle.
Perimeter of rectangle = 2( length + width )
[tex]=2(x+y)[/tex]
Also, perimeter of rectangle is equal to 56 m.
So,
[tex]56=2(x+y)\\x+y=28\\y=28-x[/tex]
Let A denotes area of rectangle.
A = length × width
[tex]A=xy\\=x(28-x)\\=28x-x^2[/tex]
Differentiate with respect to x
[tex]\frac{dA}{dx}=28-2x[/tex]
Put [tex]\frac{dA}{dx}=0[/tex]
[tex]28-2x=0\\2x=28\\x=14[/tex]
Also,
[tex]\frac{d^2A}{dx^2}=-2<0[/tex]
At x = 14, [tex]\frac{d^2A}{dx^2}=-2<0[/tex]
So, x = 14 is a point of maxima
So,
[tex]y=28-x=28-14=14[/tex]
Area of rectangle:
[tex]A=xy=14(14)=196\,m^2[/tex]
Length of rectangle = 14 m
Width of rectangle = 14 m
what two decimals are equivalent to 4.400
Answer:
4.4
4.40
Step-by-step explanation:
These two decimals above are equivalent to 4.400 because no matter the amount of zeroes, the numbers are the same. For example, 4.400 is also equivalent to 4.400000000000000000000000000000000. As long as the "4's" maintain the same place (ones place and tens place), the decimals will be congruent to one another.
Kyla makes a triangular school pennant. The area of the triangle is 180 square inches. The base of the pennant is z inches long. The height is 6 inches longer than twice the base length.
What is the height of the pennant? Recall the formula
A = bh.
Answer:
Height of the pennant is 30 inches.
Step-by-step explanation:
Given that:
Area of pennant = 180 sq inches
Base of pennant = z inches
Height of pennant = (2z + 6) inches
Also, it is a triangular pennant and area of a triangle can be given as:
[tex]A = \dfrac{1}{2} \times Base\times Height[/tex]
Putting the values in above formula:
[tex]180 = \dfrac{1}{2} \times z \times (2z+6)\\\Rightarrow 360 = 2z^{2} + 6z\\\Rightarrow 180 = z^{2} + 3z\\\Rightarrow z^{2} + 3z -180 = 0\\\Rightarrow z^{2} + 15z -12z -180 = 0\\\Rightarrow z(z + 15) -12(z+15) = 0\\\Rightarrow (z + 15) (z-12) = 0\\\Rightarrow z = 12\ or\ z=-15[/tex]
Value of z can not be negative, so value of Base, z = 12 inches.
Height is given as 2z + 6 so, height = 2[tex]\times[/tex]12 +6 = 30 inches
Answer:
C.30 inches
Step-by-step explanation:
Please HELP
2^8-10-15\div3=2
8
−10−15÷3=
Answer:
241
Step-by-step explanation:
We want to evaluate the expression:
[tex]2^8-10-15\div3[/tex]
We follow the order of operations: PEMDAS
Since there are no parenthesis(P), we evaluate the exponents(E)
[tex]2^8-10-15\div3=256-10-15\div3[/tex]
Next is Division (D)
[tex]256-10-15\div3=256-10-5[/tex]
We can then simplify since we have only subtraction.(S)
[tex]256-10-5=241[/tex]
Therefore:
[tex]2^8-10-15\div3=241[/tex]
what do you think 40×40 is
And tell how you got your answer
Answer:
1600
please see the attached picture for full solution
Hope it helps...
In performing a chi-square goodness-of-fit test with multinomial probabilities, the ___________ the difference between observed and expected frequencies, the higher the probability of concluding that the probabilities specified in the null hypothesis are correct.
Answer:
Step-by-step explanation:
The smaller/closer the difference between observed and expected frequencies, the higher the probability of concluding that the probabilities specified in the null hypothesis are correct concluding that the data fits that particular distribution given.
Can someone plz help me solved this problem I need help plz help me! Will mark you as brainiest!
Answer:
260
20
Step-by-step explanation:
speed of plane= p
speed of wind =w
(p+w)*3=840 p+w=840/3=280and
(p-w)*3.5=840p-w= 840/3.5= 240added up the 2 equations we get:
2p= 280+240p=260 mphthen
w= 20 mphWhat is 3 1/2 miles - 3,520 yards? (And put your answer in miles)
Answer:
3 1/2 miles is 6160 yards and 3,520 yards is 2 miles
Step-by-step explanation:
The coordinates of the points below represent the vertices of a rectangle.
P (2, 2) Q (6, 2) R (6, 5) S (2, 5)
What is the perimeter, in units of rectangle PQRS?
Answer:
18 units
Step-by-step explanation:
5+5=10
4+4=8
8+10=18 units
Answer:
14
Step-by-step explanation:
The perimeter of a rectangle is the sum of the lengths of the 4 sides of a rectangle. Since in a rectangle opposite sides are congruent, you just need to find the lengths of any two adjacent sides because adjacent sides cannot be opposite. Then add them and multiply the sum be 2 to account for the opposites sides.
Two find the distance between any two points, you can use the distance formula. If the two points lie on the same vertical line (both points have the same x-coordinate), or if the two points lie on the same horizontal line (both points have the same y-coordinate), then just subtract the different coordinates and take the absolute value.
PQ = |2 - 6| = |-4| = 4
QR = |2 - 5| = |-3| = 3
perimeter = 2(length + width)
perimeter = 2(4 + 3)
perimeter = 2(7)
perimeter = 14
How many strings can be formed by ordering the letters MISSISSIPPI which
contain the substring of MISS?
Answer:
1680 is the answer.
Step-by-step explanation:
Here, we have 11 letters in the word MISSISSIPPI.
Repetition of letters:
M - 1 time
I - 4 times
S - 4 times
P - 2 times
As per question statement, we need a substring MISS in the resultant strings.
So, we need to treat MISS as one unit so that MISS always comes together in all the strings.
The resultant strings will look like:
xxxxMISSxxx
xxMISSxxxxx
and so on.
After we treat MISS as one unit, total letters = 8
Repetition of letters:
MISS - 1 time
I - 3 times
S - 2 times
P - 2 times
The formula for combination of letters with total of n letters:
[tex]\dfrac{n!}{p!q!r!}[/tex]
where p, q and r are the number of times other letters are getting repeated.
p = 3
q = 2
r = 2
So, required number of strings that contain MISS as substring:
[tex]\dfrac{8!}{3!2!2!}\\\Rightarrow \dfrac{40320}{6\times 2 \times 2}\\\Rightarrow 1680[/tex]
So, 1680 is the answer.
The U.S. Commission on Crime randomly selects 600 files of recently committed crimes in an area and finds 380 in which a firearm was reportedly used. Find a 95% confidence interval for p, the true fraction of crimes in the area in which some type of firearm was reportedly used.
Answer:
95% confidence interval for p, the true fraction of crimes in the area in which some type of firearm was reportedly used.
(0.59445 , 0.67155)
Step-by-step explanation:
Explanation:-
Given random sample size 'n' = 600
sample proportion
[tex]p^{-} = \frac{x}{n} = \frac{380}{600} = 0.633[/tex]
95% of confidence interval for Population proportion is determined by
[tex](p^{-} - Z_{\frac{\alpha }{2} } \sqrt{\frac{p^{-} (1-p^{-} )}{n} } , p^{-} +Z_{\frac{\alpha }{2} } \sqrt{\frac{p^{-} (1-p^{-} )}{n} })[/tex]
Level of significance : α = 0.05
[tex]z_{\frac{0.05}{2} } = Z_{0.025} =1.96[/tex]
[tex](0.633 - 1.96 \sqrt{\frac{0.633 (1-0.633 )}{600 }}, (0.633 + 1.96 \sqrt{\frac{0.633 (1-0.633 )}{600 }[/tex]
On calculation , we get
(0.633 - 0.03855 , (0.633 + 0.03855)
(0.59445 , 0.67155)
Conclusion:-
95% confidence interval for p, the true fraction of crimes in the area in which some type of firearm was reportedly used.
(0.59445 , 0.67155)
In a science class, 40% of the students received a grade of A, 30% received a grade of B, and 20% received a grade of C on a project. The others fell short of a passing grade. a. If 12 students received an A, how many students were in the science class? b. How many students received a failing grade?
Answer:
30 students are in the science class and 3 students recieved a failing grade.
Answer:
30, 3
Step-by-step explanation:
a. Let's call the total students x. If 40% x = 12, 0.4x = 12, x = 12/0.4 = 30 students.
b. We know that 100 - 40 - 30 - 20 = 10% of all students failed. This is 10% * 30 = 0.1 * 30 = 3 students.
I can’t figure this out it’s difficult for can anyone help me Plz
Answer:
the correct option is D
Step-by-step explanation:
JK IS longer than JL
A company has a policy of retiring company cars; this policy looks at number of miles driven, purpose of trips, style of car and other features. The distribution of the number of months in service for the fleet of cars is bell-shaped and has a mean of 64 months and a standard deviation of 7 months. Using the empirical (68-95-99.7) rule, what is the approximate percentage of cars that remain in service between 43 and 50 months?
Answer:
[tex] z =\frac{50-64}{7}= -2[/tex]
[tex] z =\frac{43-64}{7}= -3[/tex]
We know that within two deviations from the mean we have 95% of the data from the empirical rule so then below 2 deviation from the mean we have (100-95)/2 % =2.5%. And within 3 deviations from the mean we have 99.7% of the data so then below 3 deviations from the mean we have (100-99.7)/2% =0.15%
And then the final answer for this case would be:
[tex] 2.5 -0.15 = 2.35\%[/tex]
Step-by-step explanation:
For this case we have the following parameters from the variable number of motnhs in service for the fleet of cars
[tex] \mu = 64, \sigma =7[/tex]
For this case we want to find the percentage of values between :
[tex] P(43< X< 50)[/tex]
And we can use the z score formula given by:
[tex] z = \frac{X-\mu}{\sigma}[/tex]
In order to calculate how many deviation we are within from the mean. Using this formula for the limits we got:
[tex] z =\frac{50-64}{7}= -2[/tex]
[tex] z =\frac{43-64}{7}= -3[/tex]
We know that within two deviations from the mean we have 95% of the data from the empirical rule so then below 2 deviation from the mean we have (100-95)/2 % =2.5%. And within 3 deviations from the mean we have 99.7% of the data so then below 3 deviations from the mean we have (100-99.7)/2% =0.15%
And then the final answer for this case would be:
[tex] 2.5 -0.15 = 2.35\%[/tex]
Solve the equation 4c=3
c =
Answer:−2x=−8
4sin2(x)−1=0
2x+3=3
Step-by-step explanation:
In a certain area an average of 13 new swarms of honeybees are seen each spring. If the number of swarms stays constant each year, what is the probability of observing between 9 and 15 (inclusive) swarms?
Answer:
The probability of observing between 9 and 15 (inclusive) swarms is 0.6639.
Step-by-step explanation:
The random variable X can be defined as the number of swarms of honeybees seen each spring.
The average value of the random variable X is, λ = 13.
A random variable representing the occurrence of events in a fixed interval of time is known as Poisson random variables.
For example, the number of customers visiting the bank in an hour or the number of typographical error is a book every 10 pages.
So, the random variable X follows a Poisson distribution with parameter λ = 13.
The probability mass function of X is as follows:
[tex]P(X=x)=\frac{e^{-\lambda}\ \lambda^{x}}{x!}; x=0,1,2,3...[/tex]
Compute the the probability of observing between 9 and 15 (inclusive) swarms as follows:
P (9 ≤ X ≤ 15) = P (X = 9) + P (X = 10) + P (X = 11) + ... + P (X = 15)
[tex]=\sum\limits^{15}_{x=9}{\frac{e^{-\lambda}\ \lambda^{x}}{x!}}\\\\=0.06605+0.08587+0.10148+0.10994\\+0.10994+0.10209+0.08848\\\\=0.66385\\\\\approx 0.6639[/tex]
Thus, the probability of observing between 9 and 15 (inclusive) swarms is 0.6639.
