1. Let x represent the length of all baseball games in the major leagues. Suppose x has a distribution that is approximately normal with a mean length of 2.9 hours and a standard deviation of 0.5 hours. To estimate the length of baseball games in the major leagues, game officials use the average length, of a random sample of 36 games. A. Determine the mean and standard deviation of the sampling distribution of the sample mean Round the standard deviation to the thousandths place (third decimal place.) B. Is the distribution of x normal? Explain. C. Draw and label a sketch of the distribution ofx.

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1. Let x represent the length of all baseball games in the major leagues. Suppose x has a
distribution that is approximately normal with a mean length of 2.9 hours and a standard
deviation of 0.5 hours. To estimate the length of baseball games in the major leagues, game
officials use the average length, of a random sample of 36 games.
A. Determine the mean and standard deviation of the sampling distribution of the sample
mean Round the standard deviation to the thousandths place (third decimal place.)
B. Is the distribution of x normal? Explain.
C. Draw and label a sketch of the distribution of x.
D. What is the probability that the average length of a random sample of 36 games is greater
than 3.1 hours? Shade the area on the sampling distribution and show your calculations.
Transcribed Image Text:1. Let x represent the length of all baseball games in the major leagues. Suppose x has a distribution that is approximately normal with a mean length of 2.9 hours and a standard deviation of 0.5 hours. To estimate the length of baseball games in the major leagues, game officials use the average length, of a random sample of 36 games. A. Determine the mean and standard deviation of the sampling distribution of the sample mean Round the standard deviation to the thousandths place (third decimal place.) B. Is the distribution of x normal? Explain. C. Draw and label a sketch of the distribution of x. D. What is the probability that the average length of a random sample of 36 games is greater than 3.1 hours? Shade the area on the sampling distribution and show your calculations.
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