Sampling Distribution of the Sample Mean — Unit test Answers

A conference consists of 5 sessions: A, B, C, D, and E. Here are the costs of the sessions.Session A: $50Session B: $50Session C: $100Session D: $150Session E: $200

The weights of bunches of bananas in the grocery store are Normally distributed with a mean weight of 3.54 pounds and a standard deviation of 0.64 pounds. A random sample of four bunches is taken and the mean weight is recorded. Which of the following is the standard deviation of the sampling distribution for the mean of all possible samples of size four?

The time needed to broil cauliflower is approximately Normally distributed with a mean of 6 minutes and a standard deviation of 1.9 minutes. If a random sample of 100 batches of cauliflower is selected, what is the probability the mean broiling time is more than 6.5 minutes?

The distribution of the number of items washed in a standard load of laundry is skewed left with a mean of 41 items and a standard deviation of 7.7 items. What is the probability that 50 randomly selected loads of laundry have a mean of more than 39.5 items?

The proportion of students at a large high school who live within five miles of the school is p = 0.19. The principal takes a random sample of 17 students from this school. Which is the best description of the shape for the sampling distribution of ?

In a large high school, 37% of the teachers believe that five minutes is not enough time for students to change classes. However, 89% of the students believe that five minutes is not enough time for students to change classes. Let and be the sample proportions of teachers and students, respectively, who believe that five minutes is not enough time for students to change classes. Suppose 28 teachers and 100 students are selected at random and asked their opinion on the amount of time students have to change class.Which of the following is the mean of the sampling distribution of ?

In a large high school, 37% of the teachers believe that five minutes is not enough time for students to change classes. However, 89% of the students believe that five minutes is not enough time for students to change classes. Let and be the sample proportions of teachers and students, respectively, who believe that five minutes is not enough time for students to change classes. Suppose 28 teachers and 100 students are selected at random and asked their opinion on the amount of time students have to change class.Which of the following is the correct shape and justification of the sampling distribution of ?

A conference consists of 5 sessions: A, B, C, D, and E. Here are the costs of the sessions.Session A: $50Session B: $50Session C: $100Session D: $150Session E: $200Here is a graph of the cost of all 5 sessions.A participant plans to attend 3 sessions. Here is a list of all possible samples of size 3 sessions from this population of 5 sessions: ABC, ABD, ABE, ACD, ACE, ADE, BCD, BCE, BDE, and CDE.Here is a graph displaying the minimum session cost for each possible sample of 3 sessions.The participant chooses 3 sessions at random from the list of all 5 sessions. The result of the random selection is sessions B, D, and E.Here is a graph displaying the distribution of session cost for this sample.

A real estate agent has 4 homes for sale: A, B, C, and D. Here are the listing prices.Home A: $150,000Home B: $250,000Home C: $190,000Home D: $550,000The agent wants to randomly select 2 of the 4 homes to show in an open house this coming weekend. This means the agent may show home A and B, A and C, A and D, B and C, B and D, or C and D. Which of the following gives the sampling distribution of the sample mean listing price for all possible samples of size 2 from this population of 4 homes?

The ages of the 5 officers for a school club are 18, 18, 17, 16, and 15. The minimum of the ages of the officers is 15. The table displays all possible samples of size 2 and the corresponding minimum for each sample.Using the minimums in the table, is the sample minimum an unbiased estimator?

A café wants to study how customers tip differently based on what they order. The distribution of tips given by customers who buy only a cup of coffee is bimodal with a mean of $0.29 and a standard deviation of $0.116. The distribution of tips given by customers who buy only a salad is approximately Normally distributed with a mean of $2.89 and a standard deviation of $1.18. If a random sample of 35 tips from customers who buy only a cup of coffee is selected and a random sample of 20 customers who buy only a salad is selected, what is the probability of a sample mean being at least $2.50 more for customers who buy only a salad than for those who buy only a cup of coffee?

A student would like to estimate the mean length of words in a book report he just finished writing. He selects a random sample of 20 words and determines the mean length to be 4 characters. Later, he discovers how to use a built-in function of his word-processing program that reveals that the mean length of all words in his book report is 4.3 characters. Which of the following describes the number, 4.3?

A bottled water company bottles varying sizes of water, from 8-ounce to 1-gallon containers. The company has determined that the mean quantity in their 20-ounce bottles is 20.8 ounces with a standard deviation of 0.6 ounces. The bottling plant manager believes his machines are overfilling the bottles. A random sample of 30 bottles is taken, and the mean number of ounces of water is recorded. Which of the following values of the mean of the sample is most likely to occur if the true mean number of ounces is 20.8?

At a university, 34% of undergraduate students love spicy food, while 45% of graduate students love spicy food. Let and be the sample proportions of undergraduate and graduate students at this university, respectively, who love spicy food. Suppose 35 undergraduate students and 28 graduate students from this university are selected at random and asked if they love spicy food.Which of the following is the correct calculation and interpretation of the standard deviation of the sampling distribution of ?

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 mean of the sampling distribution of ?