Exam 10: Sampling Distributions

McCain Foods (Canada) of New Brunswick produces frozen French fries. Suppose one line of fries has an average length of 7.62 centimetres with a standard deviation of 1.27 centimetres. To make sure that the quality standard is met, they plan to select a random sample of n = 100 fries each day. Yesterday, the sample mean was 7.75 centimetres. What is the probability that the mean would be 7.75 centimetres or more if they are meeting the quality standards?

According to the local real estate board, the average number of days that homes stay on the market before selling is 78.4, with a standard deviation equal to 11 days. A prospective seller selected a random sample of 36 homes from the multiple listing service. Above what value for the sample mean should 95 percent of all possible sample means fall?

It is believed that 40% of all medical doctors in Canada are women. Suppose that a random sample of 100 doctors is selected. Find the probability that at least 50% of this sample will be women.

It is generally believed that electrical problems affect about 14% of new cars. An automobile mechanic conducts diagnostic tests on 128 new cars on the lot. a. Describe the sampling distribution of the sample proportion by naming the model and telling its mean and standard deviation. b. What is the probability that in this group over 18% of the new cars will be found to have electrical problems?

Consider the following to answer the question(s) below: In a metal fabrication process, metal rods are produced that have an average length of 20.5 metres with a standard deviation of 2.3 metres. A quality control specialist collects a random sample of 30 rods and measures their lengths. -Suppose the resulting sample mean is 19.5 metres. Which of the following statements is true?

Which of the following is not an assumption or condition for the distribution of sample proportions?

A company has determined that the mean number of days it takes to collect on its accounts receivable is 36, with a standard deviation of 11 days. The company plans to select a random sample of n = 12 accounts and compute the sample mean. Which of the following statements holds true in this situation?

Consider the following to answer the question(s) below: The owner of a small convenience store is trying to decide whether to discontinue selling magazines. He suspects that only 5% of the customers buy magazines and thinks that he might be able to sell something more profitable. Before making a final decision, he keeps track of the number of customers who buy magazines each day. On a typical day he has 280 customers in his store. -On a typical day, what would be the standard deviation of the number of customers who buy magazines?

A small business ships specialty homemade candies to anywhere in the world. Past records indicate that orders weigh an average of 118 grams with a standard deviation of 14 grams. Suppose a random sample of 50 current orders is selected and each weighed. a. Describe the sampling distribution of the sample mean by naming the model and telling its mean and standard deviation. b. Suppose the resulting sample mean is 110 grams. Do you think that this sample result is unusually small? Explain.

Which of the following is not an assumption or condition for the CLT?

Consider the following to answer the question(s) below: In a metal fabrication process, metal rods are produced that have an average length of 20.5 metres with a standard deviation of 2.3 metres. A quality control specialist collects a random sample of 30 rods and measures their lengths. -Which of the following statements is (are) true about the sampling distribution of the sample mean?

A claim was recently made on national television that two of every three doctors recommend a particular pain killer. Suppose a random sample of n = 300 doctors revealed that 180 said that they would recommend the painkiller. If the TV claim is correct, what is the probability of 180 or fewer in the sample agreeing?

What are the two assumptions and three conditions of the Central Limit Theorem? Explain each of them.

In a metal fabrication process, metal rods are produced that have an average length of 20.5 metres with a standard deviation of 2.3 metres. A quality control specialist collects a random sample of 30 rods and measures their lengths. a. Describe the sampling distribution of the sample mean by naming the model and telling its mean and standard deviation. b. Suppose the resulting sample mean is 19.5 metres. Do you think that this sample result is unusually small? Explain.

It is believed that on average, households spend $150 a week on groceries with a standard deviation of $50. What is the probability that in a sample of 64 households, the average amount spent on groceries will be no more than $140 per week?

Which of the following statements is true with respect to the sampling distribution of a proportion?

Suppose that in a recent survey, about 33% of Canadians polled said that they would likely purchase reusable cloth bags for groceries in order to reduce plastic waste. Suppose 45 shoppers are interviewed at a local supermarket. a. Describe the sampling distribution of the sample proportion by naming the model and telling its mean and standard deviation. b. What is the probability that no more than 12 shoppers will say that they are likely to purchase reusable cloth bags for groceries?

Ian's Tree Farm grows spruce trees for plant nurseries. The average annual increase in tree diameter is 7.9 centimetres with a standard deviation of 1.3 centimetres. A random sample of n = 50 trees is collected. What is the probability of the sample mean being less the 7.4 centimetres?

Consider the following to answer the question(s) below: According to a recent survey, about 33% of Canadians polled said that they would likely purchase reusable cloth bags for groceries in order to reduce plastic waste. Suppose 45 shoppers are interviewed at a local supermarket. -What is the probability that no more than 12 shoppers will say that they are likely to purchase reusable cloth bags for groceries?

Suppose that it is believed that 40% of adults have a company pension. If 100 adults are surveyed, a. What is the probability of finding a sample with less than 30 adults having a company pension? b. What is the probability of finding no more than 45 adults having a company pension?