Answer:
0.989 = 98.9% probability that Mr. Bateman’s class has more students who pass on the first try
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution, the binomial approximation to the normal and subtraction of normal distributions.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Subtraction of normal distributions:
When two normal variables are subtracted, the mean is the subtraction of the means while the standard deviation is the square root of the sum of the variances.
Among Mr. Adams’s students, 68% pass the driving test on the first try. Sample of 40.
This means that [tex]p = 0.68, n = 40[/tex].
[tex]\mu_A = np = 40*0.64 = 27.2[/tex]
[tex]s_A = \sqrt{40*0.68*0.32} = 2.95[/tex]
74% of Mr. Bateman’s students pass the driving test on the first try. Sample of 50:
[tex]p = 0.74, n = 50[/tex]
[tex]\mu_B = np = 50*0.74 = 37[/tex]
[tex]s_B = \sqrt{50*0.74*0.26} = 3.1016[/tex]
What is the probability that Mr. Bateman’s class has more students who pass on the first try?
This is the probability that B - A is greater than 0.
Distribution B - A:
Mean:
[tex]\mu = \mu_B - \mu_A = 37 - 27.2 = 9.8[/tex]
Standard deviation:
[tex]\sigma = \sqrt{s_A^2 + s_B^2} = \sqrt{2.95^2 + 3.1016^2} = 4.28[/tex]
Probability of being larger than 0:
1 subtracted by the pvalue of Z when X = 0. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0 - 9.8}{4.28}[/tex]
[tex]Z = -2.29[/tex]
[tex]Z = -2.29[/tex] has a pvalue of 0.011
1 - 0.011 = 0.989
0.989 = 98.9% probability that Mr. Bateman’s class has more students who pass on the first try
Answer:
0.734, c
Step-by-step explanation:
Sarah earned $12 per hour babysitting.
Sarah babysits 15 hours each week.
she receives a 7%pay increase.
How much more money will Sarah earn each week
after the pay increase?
Answer:
She makes 192.6$$
Step-by-step explanation:
A window washer earns $4 per window. Which equation represents the relationship between his total earnings and the number of windows he washes?
ANSWER ASAP PLS
The circular opening of a tunnel has a circumference of 36 meters. Which equation can be used to find d, the
diameter of the tunnel opening in meters?
Heeeeeelp! I’m literally so behind
Answer:
That would be 9 my good sir ( or ma'am )
Step-by-step explanation:
basicly round the 61 so that there would not be a remainder and divide 54 by 6 you will get 9, so therefore the same case is for 540 by 60.
Have a nice day
write an equation for the nth term of the arithmetic sequence. Then find a40.
1/4,1/2,3/4,1,...
Answer:
The nth term is: [tex]a_n = \frac{1}{4} + \frac{1}{4}(n-1)[/tex]
a40 = 10
Step-by-step explanation:
Arithmetic sequence:
In an arithmetic sequence, the difference between consecutive terms is always the same, and this difference is called common difference.
The nth term of a sequence is given by:
[tex]a_n = a_1 + (n-1)d[/tex]
In which [tex]a_1[/tex] is the first term and d is the common difference.
1/4,1/2
This means that:
[tex]d = \frac{1}{2} - \frac{1}{4} = \frac{2}{4} - \frac{1}{4} = \frac{1}{4}[/tex]
1/4
This means that [tex]a_1 = \frac{1}{4}[/tex]
The nth term is:
[tex]a_n = a_1 + (n-1)d[/tex]
[tex]a_n = \frac{1}{4} + \frac{1}{4}(n-1)[/tex]
Then find a40.
[tex]a_{40} = \frac{1}{4} + \frac{1}{4}(40-1) = \frac{1}{4} + \frac{39}{4} = \frac{40}{4} = 10[/tex]
So
a40 = 10
Roseanne drew a circle with a radius of 20.2 cm. What was the approximate circumference of the circle if you use 3.14 for ?
A. 63.428 cm
B. 126.856 cm
C. 126.956 cm
D. 253.712 cm
2
Sierra's ice cream shop made $45 before she had to close early when the power went out. She realized she lost ſ of
a dollar each hour when the shop was closed. The expression that models this situation is 45 - an what was Sierra's
profit if the shop was closed for 6 hours?
$24
O $36
O $41
$49
Answer:
if shes losing 2/3 each hour, the her profit would be 41.
Step-by-step explanation:
2/3 x 6 is 4, 45 - 4 is 41.
Find the measure of <5.
45 = [?]
69%
25
Answer:
Solution given:
<5+69°=180°[co- interior angle]
<5=180°-69°=111°
<5=111°
What is the approximate average rate of change of the function f(x) = -20(1.3)x^
over the interval 1.2 _< x _< 2.7?
Answer:
c
Step-by-step explanation:
Find the product? y ^4 · y ^3
Answer:
if it will help
y^7
Step-by-step explanation:
y^4+3 = y^7
determine the point-slope form of the line with slope -7 that intersects the point (5,23)
Answer:
y=-7x+58
Step-by-step explanation:
A philanthropic organization helped a town in Africa dig several wells to gain access to clean water. Before the wells were in place, an average of 120 infants contracted typhoid each month. After the wells were installed, the philanthropic organization surveyed for nine months and found an average of 90 infants contracted typhoid per month. Assume that the population standard deviation is 40 and the number of infants that contract typhoid is normally distributed. Specify the null and alternative hypotheses to determine whether the average number of infants that contract typhoid has decreased because the wells were put in place.
Answer:
H0 : μ = 120
H1 : μ < 120
We Can conclude that the number of infants that contract typhoid has reduced because the wells were put in place.
Step-by-step explanation:
Average Number of infants who contracted typhoid monthly = 120
Average Number of infants who contracted typhoid monthly after well installation = 90
The null and alternative hypothesis :
H0 : μ = 120
H1 : μ < 120
Obtain the test statistic :
(Xbar - μ) ÷ s/sqrt(n)
(90 - 120) ÷ 40/sqrt(9)
-30 ÷ 13.3333
= - 2.25
The Pvalue at 95% confidence, df = n-1 = 9 - 1 = 8
Tcritical at 95%, df = 8 ; one tailed = 0.02728
Decision region :
Pvalue < α ; Reject H0
0.02728 < 0.05 ; Hence, we conclude that there is significant evidence that the average number of infants that contract typhoid has decreased because the wells were put in place.
What are the first three terms of the sequence defined by the following equation?
an = 2 • (-3)n - 1.
Answer:
-7, -13, -19
Step-by-step explanation:
plug in 1,2, and 3 into the part of the equation "n".
Answer:
a1 = -7
a2 = - 13
a3 = - 19
Step-by-step explanation:
n = 1
a1 = 2*(-3)*1`- 1
a1 = -6 - 1
a1 = - 7
n=2
a2 = 2(-3)*2 - 1
a2 = -12 -1
a2 = - 13
n3 = 2(-3)*3 - 1
n3 = -18 - 1
n3 = -19
Each term is - 6 away from the previous one.
Maria's earns $1700 per month and gets a commission rate of 15% of the jewelry she sells. If she sold $23000 worth of jewelry this month, what is her montly earnings?
Answer:
$5150
Step-by-step explanation:
1700+0.15(23000)
$5150
Please help! And please explain how you did it!
Answer:
<
Explanation:
turn 5/11 into a decimal: 0.45 which is LESS than 0.50 (0.5).
Answer:
<
Step-by-step explanation:
When comparing fractions and decimals/fractions and percentages/decimals and percentages, it's always good to convert them to have the same type on either side. However, you don't really need to with this problem.
Here's a trick: the larger the denominator is in a fraction, the smaller the value of the fraction is. If the fraction on the left were 5/10, then we know that it would be equal to 0.5 (you can convert either one). Now, since the denominator of the fraction is one greater than 10, we know that the fraction's value is just a little bit less than 5/10. This makes the fraction less than 0.5.
I hope it made sense. Brainliest would be cool but no worries.
If the two spinners below are spun, what is the probability that the numbers will add to more than 4?
The image of the labeled spinner isn't attached
Answer:
Kindly check explanation
Step-by-step explanation:
Answering hypothetically ;
First create a sample space using the label of the two spinners ;
Each space will be the sum of the possible number that shows up on each turn of the spinner.
From the sample space, count the number of spaces where, the sun is greater than 4, that is the required outcome ; = x
Then the total number of samples in the sole space = total possible outcomes = y
Hence,
P(obtaining a sum greater than 4) = required outcome / Total possible outcomes
= x / y
-4.5 + 4.4 + ____ = 0
What’s missing?
-6.7 + 6.8
-6.7 + (-6.6)
7.2 + (-7.2)
7.2 + (-7.3)
Answer:
-6.7+6.8
Step-by-step explanation:
‐4.5+4.4+x=0====> -0.1+x=0===> x= 0.1
so we are looking for the choice with the answer of 0.1
-6.7+6.8=0.1✔
-6.7+(-6.6)= -13.3❌
7.2+(-7.2)=0❌
7.2+(-7.3)=(-0.1)❌
Gerri is working on a project that needs to be halfway completed by Friday. So far, she has completed of the project. How much of the project does she have to finish by Friday?
Answer:
So far Gerri is 1/3 complete and needs to be 1/2 complete by Friday. In order to find how much needs finished by Friday, we subtract the fractions.
1/2 - 1/3
1/2 + (-1/3)
3/6 + (-2/6)
(3+(-2))/6
1/6
Hope this helps
How to solve (x+7)(x-9)>0
9514 1404 393
Answer:
(x < -7) ∪ (x > 9)
Step-by-step explanation:
The zeros of the function are the values of x that make the factors zero.
x +7 = 0 ⇒ x = -7
x -9 = 0 ⇒ x = 9
When this is expanded, we can see that the leading coefficient is positive.
x² -2x -63 > 0
This means the parabola opens upward. It will be greater than 0 for x-values to the left of the left zero, and to the right of the right zero. (It is less than zero between those values.)
The solution is x < -7 or x > 9.
_____
In general, for polynomial inequalities, look for the locations of the zeros. The sign of the polynomial will have the sign of the leading coefficient for values of x to the right of the right-most zero. (Here, positive for x > 9.) As you progress farther to the left along the number line, the polynomial changes sign at each zero.
Here, the polynomial becomes negative between the values x=9 and x=-7. Then it is positive again for x < -7.
HELP ASAP NO LINKS
What is the solution to the equation X=
56 8
co
O x = 448
Ox=64
O x = 48
Ox=7
Answer:
the answer is x=7 cause you have to divide 56 by 8 and that will give you 7 cause 8×7=56
How would you decide whether or 5 or 595 is greater?
Answer:
Well, the number 595 is exceptionally larger. You would be able to tell by simply subtracting 595 and 5 and you would get 590 leaving you with answer. 595 is greater
Step-by-step explanation:
Selena is a freelance graphic artist who charges $65 per hour for her services. A client paid her $195 for her last project. The equation below represents this situation.
65h = 195
For how many hours did Selena work on that project?
Answer: 3 hours
Step-by-step explanation:
195/65=3
Answer:
3
Step-by-step explanation:
$195 divided by $65 is 3 hours of work
what is the slope line according to the image
PLZ ANSWER QUIKCLY
Which expression is equivalent to -12(3x-3/4)
-36x-8
-36x + 8
-36x-9
-36x +9
Answer:
Last one, -36x+9.
Explanation: You need to multiply negative times positive which is negative. But look at the last one -12×-3/4 equals positive 36/4 which equals 9.
I just need help with this is anyone can help I would be happy Thx
Answer:
24 sq cm
Step-by-step explanation:
the big square is 20 and the small one is 4
The diameter of a circle is 14cm. Which TWO statements are correct?
A
Answer:
(a) and (e)
Step-by-step explanation:
Given
[tex]d = 14cm[/tex]
Required
Select the true statements
First, is a statement about the area.
The area is calculated as:
[tex]Area= \pi*\frac{d^2}{4}[/tex]
So, we have:
[tex]Area= 3.14*\frac{14^2}{4}[/tex]
[tex]Area= 3.14*49[/tex]
(a) is true
Next, is a statement about the circumference.
This is calculated as:
[tex]C = \pi d[/tex]
So, we have:
[tex]C = 3.14 * 14[/tex]
(e) is true
Roy collected 30 Avenger stickers. He gave 3/5 of them to her friends. How many stickers did he give to his friends
Answer:
29.4
Step-by-step explanation:
then convert to whole number
Find the volume.
PLEASE HELP I WILL GIVE BRAINLIEST TO THE RIGHT ANSWER
Due in 10 min plz help
Answer:
9 cm
Step-by-step explanation:
Answer:
9cm
Step-by-step explanation:
Help please I’m confused
Answer:
x=4 and y = 3 ...answer : 1
Step-by-step explanation:
hello :
x/8 =5/10 means : x=40/10 so: x=4
y/6 =5/10 means : y=30/10 so: y=3
