Question 1

Find the shaded area under the standard normal curve.

A)0.8944
B)0.1056
C)0.3944
D)0.0528

Accepted Answer

B

Question 2

Find the z-scores that bound the middle 74% of the area under the standard normal curve.
A)-1.13, 1.13
B)-1.24, 1.24
C)-0.99, 0.99
D)-1.07, 1.07

Accepted Answer

The middle 74% under the standard normal curve leaves 13% in each tail (since 100% - 74% = 26%, and 26%/2 = 13%). Looking up 13% in the z-table or using a calculator to find the z-score that corresponds to the cumulative area of 0.87 (since 0.13 + 0.74 = 0.87), we find z-scores of approximately -1.13 and 1.13.

Question 3

Find ${ } ^ { z } 0.09$
A)  1.44 
B)  1.34 
C)  1.08 
D)  1.51

Accepted Answer

B

Question 4

The following figure is a probability density curve that represents the lifetime, in months, of a certain type of laptop battery. 
  
Find the proportion of batteries with lifetimes less than 20 months.
A)0.24
B)0.25
C)0.75
D)0.49

Accepted Answer

The answer of The following figure is a probability density...

Question 5

Find the shaded area under the standard normal curve.
A)0.5122
B)0.9878
C)0.4878
D)0.2439

Accepted Answer

The answer of Find the shaded area under the standard...

Question 6

A normal population has a mean $\mu = 10$ and standard deviation $\sigma = 2$ What is the 86 th percentile of the population?
A)  10.94 
B)  9.73 
C)  13.38 
D)  12.16

Accepted Answer

The 86th percentile corresponds to a z-score of approximately 1.08. Using the formula $X = \mu + z\sigma$, we calculate $X = 10 + 1.08 \times 2 = 12.16$.

Question 7

The following figure is a probability density curve that represents the lifetime, in months, of a certain type of laptop  
Find the proportion of batteries with lifetimes between 10 and 20 months
A)0.74
B)0.06
C)0.26
D)0.20

Accepted Answer

The answer of  The following figure is a probability...

Question 8

Find the area under the standard normal curve that lies outside the interval between z = -2.2 and z = -1.3.
A)0.4032
B)0.9171
C)0.0829
D)0.5968

Accepted Answer

The answer of  Find the area under the standard...

Question 9

Find the area under the standard normal curve to the left of z = -0.7.
A)0.7580
B)0.2580
C)0.1210
D)0.2420

Accepted Answer

The answer of  Find the area under the standard...

Question 10

Find the z-score for which the area to the left is 0.79.
A)1.04
B)0.58
C)0.64
D)0.81

Accepted Answer

The answer of Find the z-score for which the area...

Question 11

Find the z-score for which the area to the right is 0.07.
A)1.59
B)1.35
C)1.48
D)1.74

Accepted Answer

The answer of Find the z-score for which the area...

Question 12

Find the area under the standard normal curve to the right of z = 1.6.
A)0.0548
B)0.4452
C)0.0274
D)0.9452

Accepted Answer

The area to the right of z = 1.6 under the standard normal curve can be found by subtracting the area to the left of z = 1.6 from 1. The area to the left of z = 1.6 is approximately 0.9452, so the area to the right is 1 - 0.9452 = 0.0548.

Question 13

A normal population has a mean $\mu = 27$ and standard deviation $\sigma = 9$ What proportion of the population is between 26 and 31 ?
A)  0.2138 
B)  0.7862 
C)  0.4562 
D)  0.6700

Accepted Answer

To find the proportion of the population between 26 and 31, we calculate the z-scores for 26 and 31. The z-score for 26 is $(26-27)/9 = -0.1111$ and for 31 is $(31-27)/9 = 0.4444$. Using the standard normal distribution table, the area between these z-scores is approximately 0.2138.

Question 14

Find the shaded area under the standard normal curve.

A)0.0528
B)0.3944
C)0.1056
D)0.8944

Accepted Answer

The answer of Find the shaded area under the standard...

Question 15

A normal population has a mean $\mu = 34$ and standard deviation $\sigma = 11$ What proportion of the population is less than 41 ?
A)  0.8106 
B)  1.0000 
C)  0.2611 
D)  0.7389

Accepted Answer

To find the proportion of the population less than 41, we calculate the z-score: $ z = \frac{41 - 34}{11} = \frac{7}{11} \approx 0.636 $. Using the standard normal distribution table, the cumulative probability for $ z = 0.636 $ is approximately 0.7389.

Question 16

The following figure is a probability density curve that represents the lifetime, in months, of a certain type of laptop battery.
 
What is the probability that a randomly chosen battery lasts longer than 20 months?
A)0.49
B)0.24
C)0.25
D)0.51

Accepted Answer

The answer of The following figure is a probability density...

Question 17

Find the area under the standard normal curve that lies between z = 1.8 and z = 2. 
A)0.0132
B)0.4772
C)0.5228
D)0.9868

Accepted Answer

To find the area under the standard normal curve between z = 1.8 and z = 2, we look up the cumulative area from the left up to each z-score in the standard normal distribution table or use a calculator. The area to the left of z = 1.8 is approximately 0.9641, and the area to the left of z = 2 is approximately 0.9772. Subtracting these gives the area between z = 1.8 and z = 2: 0.9772 - 0.9641 = 0.0131, which rounds to 0.0132.

Question 18

A normal population has a mean $\mu = 30$ and standard deviation $\sigma = 7$ What is the probability that a randomly chosen value will be greater than  31 ? 
A)  0.4443 
B)  0.7881 
C)  0.5557 
D)  0.7580

Accepted Answer

The probability that a randomly chosen value will be greater than 31 is 0.4443. This is because the z-score for a value of 31 is (31 - 30) / 7 = 0.1429, and the area under the normal curve to the right of a z-score of 0.1429 is 0.4443.

Question 19

A bottler of drinking water fills plastic bottles with a mean volume of 999 milliliters (mL) and standard deviation 4 mL. The fill volumes are normally distributed. What proportion of bottles have volumes greater than 994 mL?
A)1.0000
B)0.8944
C)0.9599
D)0.8925

Accepted Answer

The proportion of bottles with volumes greater than 994 mL is the area under the normal distribution curve to the right of 994 mL. Using a standard normal distribution table, we find that the area to the right of z = (994 - 999) / 4 = -1.25 is 0.8944.

Question 20

Find the shaded area under the standard normal curve.

A)0.4878
B)0.8291
C)0.1709
D)0.0854

Accepted Answer

The answer of Find the shaded area under the standard...

Quiz 7: Confidence Intervals

Find the shaded area under the standard normal curve.

Find the z-scores that bound the middle 74% of the area under the standard normal curve.

Find ${ } ^ { z } 0.09$

The following figure is a probability density curve that represents the lifetime, in months, of a certain type of laptop battery. Find the proportion of batteries with lifetimes less than 20 months.

Find the shaded area under the standard normal curve.

A normal population has a mean $\mu = 10$ and standard deviation $\sigma = 2$ What is the 86 th percentile of the population?

The following figure is a probability density curve that represents the lifetime, in months, of a certain type of laptop battery Find the proportion of batteries with lifetimes between 10 and 20 months

Find the area under the standard normal curve that lies outside the interval between z = -2.2 and z = -1.3.

Find the area under the standard normal curve to the left of z = -0.7.

Find the z-score for which the area to the left is 0.79.

Find the z-score for which the area to the right is 0.07.

Find the area under the standard normal curve to the right of z = 1.6.

A normal population has a mean $\mu = 27$ and standard deviation $\sigma = 9$ What proportion of the population is between 26 and 31 ?

Find the shaded area under the standard normal curve.

A normal population has a mean $\mu = 34$ and standard deviation $\sigma = 11$ What proportion of the population is less than 41 ?

The following figure is a probability density curve that represents the lifetime, in months, of a certain type of laptop battery. What is the probability that a randomly chosen battery lasts longer than 20 months?

Find the area under the standard normal curve that lies between z = 1.8 and z = 2.

A normal population has a mean $\mu = 30$ and standard deviation $\sigma = 7$ What is the probability that a randomly chosen value will be greater than 31 ?

A bottler of drinking water fills plastic bottles with a mean volume of 999 milliliters (mL) and standard deviation 4 mL. The fill volumes are normally distributed. What proportion of bottles have volumes greater than 994 mL?

Find the shaded area under the standard normal curve.

Quiz 7: Confidence Intervals

Find the shaded area under the standard normal curve.

Find the z-scores that bound the middle 74% of the area under the standard normal curve.

Find z0.09{ } ^ { z } 0.09z0.09

The following figure is a probability density curve that represents the lifetime, in months, of a certain type of laptop battery. Find the proportion of batteries with lifetimes less than 20 months.

Find the shaded area under the standard normal curve.

A normal population has a mean μ=10\mu = 10μ=10 and standard deviation σ=2\sigma = 2σ=2 What is the 86 th percentile of the population?

The following figure is a probability density curve that represents the lifetime, in months, of a certain type of laptop battery Find the proportion of batteries with lifetimes between 10 and 20 months

Find the area under the standard normal curve that lies outside the interval between z = -2.2 and z = -1.3.

Find the area under the standard normal curve to the left of z = -0.7.

Find the z-score for which the area to the left is 0.79.

Find the z-score for which the area to the right is 0.07.

Find the area under the standard normal curve to the right of z = 1.6.

A normal population has a mean μ=27\mu = 27μ=27 and standard deviation σ=9\sigma = 9σ=9 What proportion of the population is between 26 and 31 ?

Find the shaded area under the standard normal curve.

A normal population has a mean μ=34\mu = 34μ=34 and standard deviation σ=11\sigma = 11σ=11 What proportion of the population is less than 41 ?

The following figure is a probability density curve that represents the lifetime, in months, of a certain type of laptop battery. What is the probability that a randomly chosen battery lasts longer than 20 months?

Find the area under the standard normal curve that lies between z = 1.8 and z = 2.

A normal population has a mean μ=30\mu = 30μ=30 and standard deviation σ=7\sigma = 7σ=7 What is the probability that a randomly chosen value will be greater than 31 ?

A bottler of drinking water fills plastic bottles with a mean volume of 999 milliliters (mL) and standard deviation 4 mL. The fill volumes are normally distributed. What proportion of bottles have volumes greater than 994 mL?

Find the shaded area under the standard normal curve.

Find ${ } ^ { z } 0.09$

A normal population has a mean $\mu = 10$ and standard deviation $\sigma = 2$ What is the 86 th percentile of the population?

A normal population has a mean $\mu = 27$ and standard deviation $\sigma = 9$ What proportion of the population is between 26 and 31 ?

A normal population has a mean $\mu = 34$ and standard deviation $\sigma = 11$ What proportion of the population is less than 41 ?

A normal population has a mean $\mu = 30$ and standard deviation $\sigma = 7$ What is the probability that a randomly chosen value will be greater than 31 ?