CB.Stats.VAR-6.C: Determine the appropriateness of using the normal distribution to approximate probabilities for unknown distributions.

Determine the appropriateness of using the normal distribution to approximate probabilities for unknown distributions.

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 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.

A swimming coach tracks 100-meter freestyle times for her team. These times are approximately normally distributed with a mean of 72 seconds and a standard deviation of 2.7 seconds. A random sample of 81 swims is selected from this season's practice logs.

What is the probability that the sample mean time

\bar{x}

is between 71.4 seconds and 72.45 seconds?

P(71.4 < \bar{x} < 72.45) = ?

Round your answer to the nearest hundredth.

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