A scientist studying water quality measures the lead level in parts per billion (ppb) at each of 49 randomly chosen locations along a water line. Suppose that the lead levels across all the locations on this line are strongly skewed to the right with a mean of 17 ppb and a standard deviation of 14 ppb. Assume that the measurements in the sample are independent. What is the probability that the mean lead level from the sample of 49 measurements T is less than 15 ppb? Choose 1 answer: A) Plæ <15) = 0.02 B) Plū<15) – 0.16 C) Plē <15) 0.30 D) Plö < 15) – 0.44 E) We cannot calculate this probability because the sampling distribution is not normal.
Answers
Complete Question
The complete qustion is shown on the first uploaded image
Answer:
The correct option is B
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 49[/tex]
The mean is [tex]\mu = 17ppb[/tex]
The standard deviation is [tex]\sigma = 14 ppb[/tex]
Generally the standard error of this measurement is mathematically represented as
[tex]\sigma_z = \frac{\sigma}{\sqrt{n} }[/tex]
substituting values
[tex]\sigma_{\= x} = \frac{14}{\sqrt{49} }[/tex]
[tex]\sigma_{\= x} = 2[/tex]ppb
Now the probability that the mean lead level from the sample of 49 measurements T is less than 15 ppb represented as P(X < 15 )
Next is to find the z value
[tex]z = \frac{\mu -\sigma }{\sigma_{\= x}}[/tex]
[tex]z = \frac{15-17}{2}[/tex]
[tex]z = -1[/tex]
Now checking the z-table for the z-score of -1 we have
[tex]P(X<15) = P(Z < -1 )= 0.16[/tex]
Using the normal distribution and the central limit theorem, it is found that there is a 0.16 = 16% probability that the mean lead level from the sample of 49 measurements T is less than 15 ppb, hence option B is correct.
In a normal distribution 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]
It 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, which is the percentile of X. By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex], considering a sample size of at least 30 for a skewed variable.In this problem:
Mean of 17 ppb, hence [tex]\mu = 17[/tex].Standard deviation of 14 ppb, hence [tex]\sigma = 14[/tex].Sample of 49, hence [tex]n = 49, s = \frac{14}{\sqrt{49}} = 2[/tex]The probability that the mean lead level from the sample of 49 measurements T is less than 15 ppb is the p-value of Z when X = 15, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{15 - 17}{2}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a p-value of 0.16
0.16 = 16% probability that the mean lead level from the sample of 49 measurements T is less than 15 ppb, hence option B is correct.
For more on the normal distribution and the central limit theorem, you can check https://brainly.com/question/24663213
Related Questions
All else being equal, a study with which of the following error ranges would be
the most reliable?
A. +12 percentage points
B. 117 percentage points
C. +2 percentage points
D. 17 percentage points
Answers
A boating company charges $10 equipment fee and $5.50 per hour to rent a canoe. Which is the correct linear equation for this situation?
Answers
Answer:
[tex] y =mx +b[/tex]
Where m is the slope and b the intercept.
Using the information given the variable cost 5.5 per hour represent the slope and the fixed cost 10 represent the value of b and then our model would be given by:
[tex] y =5.5 x+ 10[/tex]
Wher y is the total cost and x the hours rented
Step-by-step explanation:
For this case we want to model the situation with a general equation given by:
[tex] y =mx +b[/tex]
Where m is the slope and b the intercept.
Using the information given the variable cost 5.5 per hour represent the slope and the fixed cost 10 represent the value of b and then our model would be given by:
[tex] y =5.5 x+ 10[/tex]
Wher y is the total cost and x the hours rented
Please help, find angle R
Answers
Step-by-step explanation:
√(7^2) + (9^2)
=√(49) + (81)
=√(130)
=11.401754251
HOPE THIS HELP YOU !!! ;))))What is the product?
(x - 3)(2x2 - 5x + 1)
N
273 - 2 + 16x + 3
2x3 - 11X2 + 16x + 3
O 2x3 - 11x2 + 16x - 3
O 2x3 - x2 + 16x - 3
Answers
The right answer is of option C
Please see the attached picture for full solution
Hope it helps
Good luck on your assignment
Answer:
[tex] = 2 {x}^{3} - 11 {x}^{2} + 16x - 3 \\ [/tex]
Step-by-step explanation:
[tex](x - 3)(2 {x}^{2} - 5x + 1) \\ x(2 {x}^{2} - 5x + 1) - 3(2 {x}^{2} - 5x + 1) \\ 2 {x}^{3} - 5 {x}^{2} + x - 6 {x}^{2} + 15x - 3 \\ = 2 {x}^{3} - 11 {x}^{2} + 16x - 3[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Lauren drinks a variety of soft drinks. Over the past month, she has had 19 diet colas, 4 cans of lemonade, and 5 cans of root beer. a. Given this history, what is the probability that her next drink will be a diet cola? Lemonade? Root beer? b. What definition of probability should be used to answer this question?
Answers
Answer:
a.
Probability of Diet Cola = 19/28
Probability of Lemonade = 4/28
Probability of Root Beer = 5/28
b. Theoretical Probability
Step-by-step explanation:
Given
Diet Cola = 19
Lemonade = 4
Root Beer = 5
Required
Probability the her next drink will be
- Diet Cola
- Lemonade
- Root beer
To calculate the probability of each of the above, first we need to calculate the total number of drinks she's had
Total = Diet Cola + Lemonade + Root Beer
Total = 19 + 4 + 5
Total = 28
The probability that her next drink can be any of the above can then be calculated.
This is calculated by dividing each outcome by the total; as follows;
Probability of Diet Cola = 19/28
Probability of Lemonade = 4/28
Probability of Root Beer = 5/28
This type of probability is referred to as theoretical probability because it makes predictions base on previous occurrence of events.
View the image.View the image.View the image.
Answers
Answer:
7098
Step-by-step explanation:
For this we need to identify the area of the garden entirely and subtract the area of the parallelogram getting our land of grass.
1) 65*110=7150
2) 13*4=52
3) 7150-52=7098
Natalie is scuba diving in the ocean. She starts 30 feet below sea level. She then dives down another 20 feet. From there, she goes up 15 feet. Which equation shows Natalie's current level?
Answers
Answer:
35
Step-by-step explanation:
30+20=50
50-15=35
(Brainliest helps)
Answer:
Answer on imagine math ;)
6. The cost price of a watch is Rs
4000. Find the marked price so
that there would be a profit of 10%
after allowing a discount of 20%.
Answers
Answer:I believe it's C
Step-by-step explanation:
help me in this question
who can solve everything the fastest
Answers
Answer:
Step-by-step explanation:
1. 90
2. 42,49
3. 2860
4. 13cm
5. 16-5=11
6. Sector
7. 1 whole no. 1 divided by 5
8. 7 and 4
9. 3/9
10.57.8
11. 19:20pm
12.
A worker is paid $2,350 monthly and has $468 withheld from each monthly paycheck. Which of the following is her annual net salary
Answers
Answer:
Annual net salary = $22,584
Step-by-step explanation:
Given:
Monthly wage = $2,350
Withheld paycheck = $468
Find:
Annual net salary = ?
Computation:
Total net salary = Monthly wage - Withheld paycheck
Total net salary = $2,350 - $468
Total net salary = $1,882
Annual net salary = Total net salary × 12
Annual net salary = $1,882 × 12
Annual net salary = $22,584
Find the value of X in the triangle
Answers
An outside angle is equal to the sum of the two opposite inside angles.
122 = x + 24
X = 122 - 24
X = 98 degrees
Which triangle is similar to triangle abc?
Answers
the one that has 65 and 54, 3rd one
Answer:
Triangle three(bottom left corner)
Step-by-step explanation:
We know one angle must be 61, as it is given. The other angle can be found by subtracting 126 from 180.
So 180-126 = 54
So the two angles we are looking for are 61 and 54.
However none of the triangles have that those numbers, so we must find the third side. Using that the sum of the angles must be 180,
180-61-54 = 65
So the third angles must be 65
So now we look for the triangle that has 2 of the following: 65, 54, 61
Triangle 3 fits this.
Please help me I have limited time plzzzz select all that apply
Answers
Answer:
B and C.
Step-by-step explanation:
just divide going all the way down starting from the number 4th spot. and if you get the same number each time, its exponential
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answers
Answer: B
Step-by-step explanation:
To find the answer, you add the two equations together
Answer:
A. x - 3
Step-by-step explanation:
Set it up like this:
(3x - 2) - (2x + 1)
Combine like terms:
3x - 2 - 2x - 1
3x - 2x = x
-2 - 1 = -3
Put it together:
x - 3
Find the range of f(x) = 3x + 2 for the domain = {1,2,3}.
Answers
Answer:
Range = {5, 8, 11}
Step-by-step explanation:
On the function f(x) = 3x + 2
For the first domain, when x = 1, f(x) = 3(1) + 2 = 3 + 2 = 5
For the second, when x = 2, f(x) = 3(2) + 2 = 6 + 2 = 8
For the third domain, when x = 3, f(x) = 3(3) + 2 = 9 + 2 = 11
Solve for v
3v-9=45
Simplify your answer as much as possible.
Answers
Answer:
v = 18
Step-by-step explanation:
3v-9=45
Add 9 to each side
3v-9+9=45+9
3v = 54
Divide each side by 3
3v/3 = 54/3
v =18
Answer:
Step-by-step explanation:
Line m has no y intercept, and it’s x intercept is(3,0). Line n has no x intercept, and it’s y intercept is (0,-4) the equation of line m is____ , and the equation of line n is ______
Answers
Answer:
x = 3y = -4Step-by-step explanation:
In order for a line to have no y-intercept, it must be parallel to the y-axis. Its equation will be of the form ...
x = constant.
If the x-intercept is (3, 0), then we must have constant = 3.
__
In order for a line to have no x-intercept, it must be parallel to the x-axis. Its equation will be of the form ...
y = constant.
If the y-intercept is (0, -4), then we must have constant = -4.
__
The equation of line m is x = 3.
The equation of line n is y = -4.
Silvie states that the sum of a rational number and an irrational number is sometimes rational and sometimes irrational. Which statement correctly describes whether Silvie is correct or incorrect?
A) Silvie is incorrect; the sum of a rational number and an irrational number is always irrational
B) Silvie is correct; the sum of a rational number and an irrational number may be rational or irrational
C) Silvie is incorrect; the sum of a rational number and an irrational number is always rational
Answers
Answer:
A) Silvie is incorrect; the sum of a rational number and an irrational number is always irrational
Step-by-step explanation:
The concept of adding rational and irrational numbers states that the result will always be irrational.
Take for instance the addition of 4.5 and 3.142857
4.5 is a rational number because it can easily be expressed in fractions while 3.142857 is irrational because it can't be expressed as a simple fraction.
The addition of these two numbers gives 7.642857
7.642857 is an irrational number.
Similarly, any sum of two numbers (rational and irrational) will always result in irrational number.
Hence, Silvie is incorrect.
Answer:
A.
Step-by-step explanation:
Silvie is incorrect; the sum of a rational number and an irrational number is always irrational
What is the solution of the system shown?
(2, 2)
(2,3)
(3, 2)
Answers
Answer:
(3,2)
Step-by-step explanation:
The solution of lines on a coordinate plane is its intersection point. In this case its (3,2)
4. In an electrical circuit it is known that the voltage V varies as the current I
(ie. that V is directly proportional to 1). It is also known that V = 36
when I = 8.
a Find a formula for V in terms of I.
b Find V when I = 14.
с Find / when V = 27.
Answers
Step-by-step explanation:
V∝I
V=kI
36=k*8
k=36/8
k=4.5
a. V=4.5I
b. V=4.5*14
V= 63
c. 27=4.5I
I=27/4.5
I= 6
How do I solve this ?
Answers
Answer:
g(-9) = 1
Step-by-step explanation:
g(-9) is the value of the function at x = -9
Go over the x = -9 and go up until you hit the blue line
Read the value of y
g(-9) = 1
The top most point of a pyramid is at the center of a cube The height of a cube is 10 inches what is the volume of the square pyramid inside the cube?
Answers
Answer:
166.67 in³
Step-by-step explanation:
If the top of the pyramid is at half of the height of 10 cm tall cube, the height of the pyramid (h) is 5 inches.
Assuming that the base of the pyramid is the same as the base of the cube, the volume of the square pyramid is given by:
[tex]V=\frac{1}{3}*B*h[/tex]
Where B is the area of the square base:
[tex]V=\frac{1}{3}*(10*10)*5\\ V=166.67\ in^3[/tex]
The volume of the square pyramid inside the cube is 166.67 in³.
r=p/4(c+k) for k, please help, thank you!
Answers
Answer:
[tex]k=\frac{-cp+4r}{p}[/tex]
Step-by-step explanation:
[tex]r=p/4(c+k)[/tex]
[tex]\frac{r}{p/4} =c+k[/tex]
[tex]\frac{r}{p/4} -c=k[/tex]
[tex]-cp+4r=kp[/tex]
[tex]\frac{-cp+4r}{p} =k[/tex]
The sum of three numbers is 81. The
Second
number is 7 more
ore than the first
number and the third number doubles the sum of the first two numbers find the range of the set of numbers
Answers
Answer:
I'm assuming that the range means the smallest number to largest number which will be 10 to 54
Step-by-step explanation:
Let x represent 1st number, y represent 2nd number and z represent 3rd number
rest of the working is in the picture attached. hope you understand it!
12
a + 5
18
Find the value of a.
A. 3
B. 5
C. 8
D. 11
Answers
What's the question asking? 12a+15(18)?
Answer:
the answer is 3
Step-by-step explanation:
An article includes the accompanying data on compression strength (lb) for a sample of 12-oz aluminum cans filled with strawberry drink and another sample filled with cola. Beverage Sample Size Sample Mean Sample SD Strawberry Drink 10 530 23 Cola 10 553 16 Does the data suggest that the extra carbonation of cola results in a higher average compression strength? Base your answer on a P-value. (Use α = 0.05.)
Answers
Answer:
Step-by-step explanation:
This is a test of 2 independent groups. The population standard deviations are not known. Let μ1 be the mean compression strength from the extra carbonation of strawberry drink and μ2 be the mean compression strength from the extra carbonation of cola.
The random variable is μ1 - μ2 = difference in the mean compression strength from the extra carbonation of strawberry drink and the mean compression strength from the extra carbonation of cola.
We would set up the hypothesis.
The null hypothesis is
H0 : μ1 = μ2 H0 : μ1 - μ2 = 0
The alternative hypothesis is
H1 : μ1 < μ2 H1 : μ1 - μ2 < 0
This is a left tailed test.
Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is
(x1 - x2)/√(s1²/n1 + s2²/n2)
From the information given,
x1 = 530
x2 = 553
s1 = 23
s2 = 16
n1 = 10
n2 = 10
t = (530 - 533)/√(23²/10 + 16²/10)
t = - 2.6
The formula for determining the degree of freedom is
df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²
df = [23²/10 + 16²/10]²/[(1/10 - 1)(23²/10)² + (1/10 - 1)(16²/10)²] = 6162.25/383.752
df = 16
We would determine the probability value from the t test calculator. It becomes
p value = 0.0097
Since alpha, 0.05 > than the p value, 0.0097, then we would reject the null hypothesis. Therefore, at 5% significance level, the data suggests that the extra carbonation of cola results in a higher average compression strength.
Based on the Census, state A has 21 fewer electoral votes for president than state B. If the total number of electoral votes for these two states is 85, find the number for each state
Answers
Answer:
state A = 32 votes, state B = 53 votes
Step-by-step explanation:
Let the number of electoral votes for state A be a and state B be b
a = b - 21
a + b = 85
Substituting a for b - 21 in the second equation
2b - 21 = 85
2b = 106
b = 53
Plugging b back in
85 - 53 = 32
What is the value of x in the equation 7x + 2y=48 , when y = 3?
x = 6
x = 7
x = 8
x = 9
Answers
sub y = 3 inside the equation.
7x + 2(3) = 48
7x = 42
x = 6
Step by Step Solution:
7x+2•3=48
7x+6=48
7x-42
X=42
How much money does the average professional football fan spend on food at a single football game? That question was posed to 60 randomly selected football fans. The sampled results show thatthe sample mean was $70.00 and prior sampling indicated that the population standard deviation was $17.50. Use this information to create a 95 percent confidence interval for the the average professional football fan spend on food at a single football game.
Answers
Answer:
$70.00 +/- $4.43
= ( $65.57, $74.43)
Therefore at 95% confidence interval (a,b) = ( $65.57, $74.43)
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Sample Mean x = $70.00
Standard deviation r = $17.50
Number of samples n = 60
Confidence interval = 95%
z(at 95% confidence) = 1.96
Substituting the values we have;
$70.00+/-1.96($17.50/√60)
$70.00+/-1.96($2.259240285287)
$70.00+/-$4.428110959163
$70.00+/-$4.43
= ( $65.57, $74.43)
Therefore at 95% confidence interval (a,b) = ( $65.57, $74.43)
Pulse rates of adult females are listed in Data Set 1 "Body Data" in Appendix B. The lowest pulse rate is 36 beats per minute, the mean of the listed pulse rates is x = 74.0 beats per minute, and their standard deviation is s = 12.5 beats per minute. a. What is the difference between the pulse rate of 36 beats per minute and the mean pulse rate of the females? b. How many standard deviations is that [the difference found in part (a)]? c. Convert the pulse rate of 36 beats per minutes to a z score. d. If we consider pulse rates that convert to z scores between -2 and 2 to be neither significantly low nor significantly high, is the pulse rate of 36 beats per minute significant?
Answers
Answer:
Step-by-step explanation:
Hello!
The variable of interest is
X: pulse rate of a female adult. (beats/min)
Mean X[bar]= 74.0 beats/min
Standard deviation S= 12.5 beats/min
The lowest pulse rate is 36 beats/min
a)
The difference between the lowest pulse rate and the mean pulse for females is: 36 - 74= -38 beats/min
b)
To calculate how many standard deviations a value of the variable is from the mean, you have to subtract the mean from it and divide by the standard deviation:
(X-X[bar])/S= (36-74)/12.5= -3.04
The minimum pulse for female adults is -3.04 standard deviations away from the mean.
c)
The z score for 36 beats/min is -3.04
Considering the region of acceptance (-2; 2), the calculated value is below its lower limit, so you can conclude that the pulse rate 36 beats/min is significantly low.
I hope this helps!
