# Statistics 14 Questions: proportion, confidence level, standard deviation, population variance

1.
An auditor wants to estimate what proportion of a bank's commercial loan files are incomplete. The auditor randomly samples 100 files and finds 9 are incomplete. Using a 95% confidence interval, estimate the true proportion of incomplete files for ALL the bank's commercial loans.

2.
An auditor wants to estimate what proportion of a bank's commercial loan files are incomplete. The auditor wants to be within 4% of the true proportion when using a 95% confidence level. How many files must the auditor sample? No estimate of the proportion is available, so use 0.5 for the population proportion.

5.
If Tom gets a 70 on a physics test where the mean is 65 and the standard deviation is 5.8, where does he stand in relation to his classmates?
A) he is in the bottom 10%
B) he is in the top 10%
C) he is in the bottom 20%
D) he is in the top 20%

7.
Let's assume you have taken 100 samples of size 64 each from a normally distributed population. Calculate the standard deviation of the sample means if the population's variance is 49.

8.
A business wants to estimate the true mean annual income of its customers. It randomly samples 200 of its customers. The mean annual income was \$52,500 with a standard deviation of \$1,800. Find a 95% confidence interval for the true mean annual income of the business' customers.

10.
In a normal distribution with mu = 25 and sigma = 3 what number corresponds to z = -3?
A) none of these
B) 18
C) 20
D) 16

11.
According to the Central Limit Theorem, how big of a sample is necessary to make sure the sampling distribution of sample means is normally distributed, if we know the underlying population is already normally distributed?

12.
The area to the left of "z" is .9976. What z score corresponds to this area?
A) -2.89
B) 2.82
C) none of these
D) 2.85

13.
Interpret a 95% confidence interval of (3.355, 3.445) for the population mean.

14.
In the standard normal distribution the mean is always ___
A) 0
B) none of these
C) 2
D) 1

16.
In the standard normal distribution the variance is always ___
A) 0
B) none of these
C) 1
D) 2

17.
The area under the standard normal curve is
A) 0
B) 1
C) none of these
D) 2

19.
An automobile safety engineer wants to estimate the mean cost to repair a Chevy Corvette involved in a 30 mile per hour head-on collision. The engineer crashes 20 Corvettes and finds the mean damage is \$16,300 with a standard deviation of \$2,330. Find a 95% confidence interval for the true mean cost to repair this type of car.

20.
A business wants to estimate the true mean annual income of its customers. The business needs to be within \$500 of the true mean. The business estimates the true population standard deviation is around \$2,300. If the confidence level is 95%, find the required sample size in order to meet the desired accuracy.

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Wilfred Graves, PhD

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Active since 2010

SB, Massachusetts Institute of Technology
MS, Stanford University
MDiv, Fuller Theological Seminary
PhD, Fuller Theological Seminary

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1.

An auditor wants to estimate what proportion of a bank’s commercial loan files are incomplete. The auditor
randomly samples 100 files and finds 9 are incomplete. Using a 95% confidence interval, estimate the true
proportion of incomplete files for ALL the bank’s commercial loans.

HTML Editor

2.

An auditor wants to estimate what proportion of a bank’s commercial loan files are incomplete. The auditor wants
to be within 4% of the true proportion when using a 95% confidence level. How many files must the auditor
sample? No estimate of the proportion is available, so use 0.5 for the population proportion.

5.
If Tom gets a 70 on a physics test where the mean is 65 and the standard deviation is 5.8, where does he stand
in relation to his classmates?

A) he is in the bottom 10%

B) he is in the top 10%

C) he is in the bottom 20%

D) he is in the top 20%

7.

Let’s assume you have taken 100 samples of size 64 each from a normally distributed population. Calculate the
standard deviation of the sample means if the population’s variance is 49.

8.

A business wants to estimate the true mean annual income of its customers. It randomly samples 200 of its
customers. The mean annual income was \$52,500 with a standard deviation of \$1,800. Find a 95% confidence
interval for the true mean annual income of the business’ customers.

HTML Editor

10.
In a normal distribution with mu = 25 and sigma = 3 what number corresponds to z = -3?

A) none of these

B) 18

C) 20

D) 16

11.

According to the Central Limit Theorem, how big of a sample is necessary to make sure the sampling distribution
of sample means is normally distributed, if we know the underlying population is already normally distributed?

HTML Editor

12.

The area to the left of "z" is .9976. What z score corresponds to this area?

A) -2.89

B) 2.82

C) none of these

D) 2.85
13.

Interpret a 95% confidence interval of (3.355, 3.445) for the population mean.

HTML Editor

14.

In the standard normal distribution the mean is always ___

A) 0

B) none of these

C) 2

D) 1

16.

In the standard normal distribution the variance is always ___

A) 0

B) none of these
C) 1

D) 2

17.

The area under the standard normal curve is

A) 0

B) 1

C) none of these

D) 2

19.

An automobile safety engineer wants to estimate the mean cost to repair a Chevy Corvette involved in a 30 mile
per hour head-on collision. The engineer crashes 20 Corvettes and finds the mean damage is \$16,300 with a
standard deviation of \$2,330. Find a 95% confidence interval for the true mean cost to repair this type of car.

HTML Editor

20.

A business wants to estimate the true mean annual income of its customers. The business needs to be within
\$500 of the true mean. The business estimates the true population standard deviation is around \$2,300. If the
confidence level is 95%, find the required sample size in order to meet the desired accuracy.
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