CB.Stats.UNC-3.R: Determine whether a sampling distribution of a sample mean can be described as approximately normal.

Determine whether a sampling distribution of a sample mean can be described as approximately normal.

Example Problems

A volleyball team tracks serve speeds. These speeds are approximately normally distributed with a mean of 50 mph and a standard deviation of 6 mph. A random sample of 16 serves is selected. We can assume the serves in the sample are independent.

What is the probability that the mean serve speed in these 16 serves

\bar{x}

is farther than 2.25 mph away from the true mean?
Round your answer to the nearest hundredth.

A volleyball league reports that

95\%

of serves land in bounds. Suppose that we took random samples of

n = 40

serves from this population and computed the proportion

\hat{p}

of serves in each sample that landed in bounds. We can assume the league's claim is true.

What will be the shape of the sampling distribution of

\hat{p}

: skewed to the left, skewed to the right, approximately normal, or uniform?

A movie theater chain tracks ticket prices across its locations. These prices are approximately normally distributed with a mean of

\$14

and a standard deviation of

\$2.5

. A random sample of 100 tickets is selected.

What is the probability that the sample mean price

\bar{x}

is within

\$0.65

of the population mean?

P(13.35 < \bar{x} < 14.65) = ?

Round your answer to the nearest hundredth.

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