Question 1

Some variable of interest has a normal distribution with a mean of 100 and a standard deviation of 10. We take a random sample of size 5.

Can we calculate the probability that the sample mean is between 95 and 120? (You do not need to actually calculate the probability for this question.)

a)Yes, and the calculated probability would be exact.

b)Yes, and the calculated probability would be approximate.

c) No.

2) Speeds of Canadian tennis star Milos Raonic's serves follow a normal distribution with mean 155 miles per hour (mph) and standard deviation 12 mph. According to the 68-95-99.7% rule, there is an approximate 99.7% chance that the average speed of a sample of four his serves will be between:

Question 9 options:

A)

149 mph and 161 mph

B)

131 mph and 179 mph

C)

137 mph and 173 mph

D)

151 mph and 159 mph

E)

143 mph and 167 mph

3)

It is known that the amount of water adults drink per day follows a normal distribution with standard deviation 250 ml. A random sample of 50 adults is selected and it is found that their mean daily water intake is 1725 ml.

What is themargin of errorfor a 95% confidence interval for the true mean daily water consumption of adults? (You do not need to calculate the confidence interval. The margin of error is simply the right side of the sign in a confidence interval.)

Keep 4 decimal places in intermediate calculations and report your final answer to2 decimal places.

question 4

The sizes of farms (in acres) in a U.S. state follow a normal distribution with known standard deviation. We would like to estimate the true mean size of all farms in the state. We measure the sizes of a random sample of farms and calculate a 95%confidence interval forto be (295, 305). What is the correctinterpretation of this interval?

A)

Approximately 95% of farms have a size between 295 and 305 acres.

B)

Approximately 95% of samples of 30 farms will have a mean size between 295 and 305 acres.

C)

The probability that the population mean is between 295 and 305 acres is 0.95.

D)

In repeated samples of the same size, 95% of similarly constructed intervals will contain the population mean.

E)

In repeated samples of the same size, 95% of similarly constructed intervals will contain the sample mean.

question 5

We would like to construct a confidence interval for the mean of some population. Which of the following combinations of confidence level and sample size will produce the narrowest interval?

A)

99% confidence, n = 35

B)

95% confidence, n = 30

C)

95% confidence, n = 35

D)

90% confidence, n = 30

E)

90% confidence, n = 35