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?

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. -The sampling distribution of the sample mean lengths is Normally distributed with a mean of 20.5 metres and standard deviation of 0.42 metres. We can say this because

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?

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.

What are the 2 assumptions and 3 conditions of the Central Limit Theorem? Explain these.

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 for 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.

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?