Sampling Distribution of the Sample Mean Answers

The times to pop a regular bag of microwave popcorn without burning it are Normally distributed with a mean time of 140 seconds and a standard deviation of 20 seconds. The times to pop a mini bag of microwave popcorn without burning it are Normally distributed with a mean time of 90 seconds and a standard deviation of 15 seconds. Suppose two independent random samples, 25 of each, are taken and the mean popping times are calculated. Let R = the popping time of a randomly selected regular-sized bag and M = the popping time of a mini-sized bag. Which of the following best describes the standard deviation of the sampling distribution of ?

The prices of houses in the US are strongly skewed to the right with a mean of $383,500 and a standard deviation of $289,321. A real estate agent takes a random sample of 10 houses and records the mean price. What is the shape of the distribution of the sample mean for all possible random samples of size 10 from this population?

The daily temperatures for the winter months in Virginia are Normally distributed with a mean of 59°F and a standard deviation of 10°F. A random sample of 10 temperatures is taken from the winter months and the mean temperature is recorded. What is the shape of the distribution of the sample mean for all possible random samples of size 10 from this population?

The salaries of professional baseball players are heavily skewed right with a mean of $3.2 million and a standard deviation of $2 million. The salaries of professional football players are also heavily skewed right with a mean of $1.9 million and a standard deviation of $1.5 million. A random sample of 40 baseball players’ salaries and 35 football players’ salaries is selected. The mean salary is determined for both samples. Let represent the difference in the mean salaries for baseball and football players. Which of the following represents the mean of the sampling distribution for ?

The daily temperatures for the winter months in Virginia are Normally distributed with a mean of 59°F and a standard deviation of 10°F. The daily temperatures for the winter months in California are Normally distributed with a mean of 64°F and a standard deviation of 12°F. Random samples of 10 temperatures are taken from the winter months for both Virginia and California. The mean temperature is recorded for both samples. Let represent the difference in the mean temperatures for the winter months in Virginia and California. Which of the following represents the standard deviation of the sampling distribution for ?

The heights of five-year-olds are Normally distributed with a mean of 42.5 inches and a standard deviation of 2.5 inches. A random sample of 16 five-year-olds is taken and the mean height is recorded. What would be the mean of the sampling distribution of all possible samples of size 16?

The prices of pants at a large clothing store chain are skewed left with a mean of $32 and a standard deviation of $20. The manager at one of the stores randomly selects 10 pairs of pants. Which of the following best describes the sampling distribution of all possible samples of size 10?

The heights of five-year-olds are Normally distributed with a mean of 42.5 inches and a standard deviation of 2.5 inches. A random sample of 16 five-year-olds is taken and the mean height is recorded. What would be the standard deviation of the sampling distribution of all possible samples of size 16?

The weights of gala apples follow a Normal distribution with a mean of 140 grams and a standard deviation of 12 grams. The owner of an apple orchard randomly selects 5 apples from the harvest and records the mean weight. What is the shape of the distribution of the sample mean for all possible random samples of size 5 from this population?

The times to pop a regular bag of microwave popcorn without burning it are Normally distributed with a mean time of 140 seconds and a standard deviation of 20 seconds. The times to pop a mini bag of microwave popcorn without burning it are Normally distributed with a mean time of 90 seconds and a standard deviation of 15 seconds. Suppose two independent random samples, 25 of each, are taken and the mean popping times are calculated. Let R = the popping time of a randomly selected regular-sized bag and M = the popping time of a mini-sized bag. Which of the following best describes the shape of the sampling distribution of ?