Q: A Cadillac Escalade's braking distance (in meters) on a dry surface is normally distributed with a mean of 48 and a standard deviation of 2.2. What braking distance represents the 96th percentile?

$$ x = 48 + (2.2 \times 1.75) = 51.85 $$ meters

Q: A nurse wants to estimate the birth weight of infants with 99% confidence and a margin of error of 0.7 grams. The standard deviation is 2.2 grams. What is the minimum sample size required?

$$ n = \left( \frac{2.575 \times 2.2}{0.7} \$$right)^2$$ = 81.225 ($$round up to 82 infants)

Question 1

A random sample of 42 college students has a mean annual earning of $$18,815 and a standard deviation of 5$$,100. Construct a 95% confidence interval for the population mean annual earnings. Which of the following is the correct confidence interval?

Accepted Answer

$$ (18815 - 1623.84, 18815 + 1623.84) = (52803.16, 34336.84) $$

Question 2

The monthly utility bills in a city are normally distributed with a mean of $$100 and a standard deviation of 12. $$What is the probability that a randomly selected utility bill is less than $70?

Accepted Answer

$$ P(x \u003c 70) = P(z \u003c -2.5) = 0.0062 $$

Question 3

A Cadillac Escalade's braking distance (in meters) on a dry surface is normally distributed with a mean of 48 and a standard deviation of 2.2. What braking distance represents the 96th percentile?

Accepted Answer

$$ x = 48 + (2.2 	imes 1.75) = 51.85 $$ meters

Question 4

A sample of 48 chauffeurs has a mean annual salary of $$31,000 and a standard deviation of 1$$,275. What is the probability that the mean annual salary is less than $30,900?

Accepted Answer

$$ P(z \u003c -0.54) = 0.2946 $$

Question 5

A random sample of 75 medical school applicants has a mean score of 34 and a standard deviation of 3.5 on the MCAT. The school claims the mean is more than 33. At the 5% level of significance, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis; there is enough evidence to support the claim.

Question 6

If the standard deviation in a confidence interval problem is doubled, what happens to the width of the confidence interval?

Accepted Answer

The confidence interval becomes wider.

Question 7

A random sample of 28 sports cars has an average annual fuel cost of $$2,218 and a standard deviation of 523. $$Construct a 90% confidence interval for the population mean annual fuel cost.

Accepted Answer

$$ (2218 - 168.32, 2218 + 168.32) = (2049.68, 2386.32) $$

Question 8

A manufacturer claims the mean activating temperature for sprinkler systems is at least 135°F. A random sample of 22 systems has a mean of 133°F and a standard deviation of 3.3°F. At the 1% level of significance, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis; there is enough evidence to reject the claim.

Question 9

A nurse wants to estimate the birth weight of infants with 99% confidence and a margin of error of 0.7 grams. The standard deviation is 2.2 grams. What is the minimum sample size required?

Accepted Answer

$$ n = \left( \frac{2.575 	imes 2.2}{0.7} \$$right)^2$$ = 81.225  ($$round up to 82 infants)

Question 10

A fitness magazine claims the mean monthly cost of joining a health club is $$25. A random sample of 18 clubs has a mean of 26.25 $$and a standard deviation of $3.23. At the 10% level of significance, what is the correct conclusion?

Accepted Answer

Fail to reject the null hypothesis; there is not enough evidence to reject the claim.

Question 11

The US Department of Agriculture claims the mean consumption of bottled water per person in the US is 32.5 gallons per year. A random sample of 100 people has a mean of 31.9 gallons and a standard deviation of 3.9 gallons. At the 2% level of significance, what is the correct conclusion?

Accepted Answer

Fail to reject the null hypothesis; there is not enough evidence to reject the claim.

Question 12

A random sample of 42 eighth graders has a mean number of hours per week watching television of 19.6 and a standard deviation of 5.1. Construct a 90% confidence interval for the population mean number of hours per week.

Accepted Answer

$$ (19.6 - 1.29 	imes \frac{5.1}{\sqrt{42}}, 19.6 + 1.29 	imes \frac{5.1}{\sqrt{42}}) = (18.31, 20.89) $$

Question 13

What is the effect on the precision of a confidence interval if the sample size is increased?

Accepted Answer

The confidence interval becomes more precise.

Question 14

A utility bill in a city is normally distributed with a mean of $$100 and a standard deviation of 12. $$What is the probability that a randomly selected bill is between $$100 and 120$$?

Accepted Answer

$$ P(100 \u003c x \u003c 120) = P(0 \u003c z \u003c 1.67) = 0.4522 $$

Question 15

A sample of 20 IQ scores has a mean score of 105.8 and a standard deviation of 15. Assume IQ scores are normally distributed. What distribution should be used to construct a confidence interval for the mean?

Accepted Answer

Normal distribution, because $$\sigma is $$known and distribution is normal.

Question 16

A pay scale for NOVA Corps is normally distributed with a mean of 1125 credits and a standard deviation of 134 credits. What is the lowest pay that would still place a member in the top 1% of pay?

Accepted Answer

$$ x = 1125 + (2.33 	imes 134) = 1282.25 $$ credits

Question 17

A random sample of 10 women has a mean height of 63.4 inches and a standard deviation of 2.4 inches. Construct a 99% confidence interval for the population mean height.

Accepted Answer

$$ (63.4 - 2.575 	imes \frac{2.4}{\sqrt{10}}, 63.4 + 2.575 	imes \frac{2.4}{\sqrt{10}}) = (61.45, 65.35) $$

Question 18

A hat company claims the mean hat size for a male is at least 7.25. A random sample of 12 men has a mean of 7.15 and a standard deviation of 0.27. At the 5% level of significance, what is the correct conclusion?

Accepted Answer

Fail to reject the null hypothesis; there is not enough evidence to reject the claim.

Statistics Practice Test Study Guide: Probability, Normal Distribution, Confidence Intervals, and Hypothesis Testing

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