CB.Stats.UNC-3.S: Interpret probabilities and parameters for a sampling distribution for a sample mean.

Interpret probabilities and parameters for a sampling distribution for a sample mean.

Example Problems

A teacher tracks individual student Blooket scores from a school-wide tournament. The scores are normally distributed with a mean of 85 points and a standard deviation of 6 points. Suppose the teacher randomly samples 4 scores and calculates the sample mean.

What is the probability that the sample mean score

\bar{x}

exceeds 90 points?

P(\bar{x} > 90) = ?

Round your answer to the nearest hundredth.

A track and field team has 144 athletes whose 400-meter times (in seconds) are normally distributed with a mean of 54.6 seconds and a standard deviation of 2.4 seconds. The coach randomly selects one-fourth of the athletes and records the sample mean of their times.

What is the probability that the sample mean time

\bar{x}

is less than 53.8 seconds?

P(\bar{x} < 53.8) = ?

Round your answer to the nearest hundredth.

A league office records shots on goal per game for varsity lacrosse teams. The shots are normally distributed with a mean of

11.5

shots and a standard deviation of

3.6

shots. Suppose we take a random sample of

144

games and calculate the sample mean.

What is the probability that the sample mean shots

\bar{x}

is farther than

0.51

shots away from the population mean?
Round your answer to the nearest hundredth.

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