1. The amount of time a bank teller spends with each customer is normally distributed with a mean of 6.0 minutes, and a standard deviation of 2.4 minutes. (a) What is the probability that the teller will spend more than 10 minutes with a customer? Make sure to define the random variable under consideration. (b) A random sample of 9 customers is selected. (1) Specify the sampling distribution for the mean of the sample. Be sure to include the mean and standard deviation of the distribution. (2) What is the probability that the average time spent per customer will be at least 5.4 minutes? (3) If time spent per customer was not normally distributed, would the result in (2) be valid? Explain.
2. The Canadian Real Estate Association (CREA) put the average price at which a house was sold in Canada in 2014 at $415 thousand. Assume further that the standard deviation of the house prices is $134 thousand. Suppose that a survey consisting of a sample of 36 homes conducted by an independent company yielded a sample mean house price of $369 thousand. (a) Find the approximate probability that the survey would have resulted in a mean price this low ($369 thousand) or lower, and comment on the validity of the result. (b) Does your result in (a) make you question the average price quoted by CREA? Explain.
3. When the British Columbia government introduced a carbon tax, it did not want to lose votes, so it guaranteed that all revenue from the carbon tax would be used to reduce income taxes. Suppose that a sample of 1000 people is to be drawn in order to estimate the proportion of British Columbians who support the tax. Let ????̂ be a random variable for the proportion of people in the sample of 1000 who support the tax. (a) If the true proportion of British Columbians who support the tax is 0.45, what is the approximate sampling distribution (including the mean and the standard deviation) for the sample proportion, ????̂? Be sure to justify your answer. (b) What is the probability that a majority (50% or more) of the people in the sample will support make their purchases with a credit card? Given this probability, is the sample outcome more likely to be factual or misleading about whether a majority of British Columbians support the tax? Explain.
1. The amount of time a bank teller spends with each customer is normally distributed with amean of 6.0 minutes, and a standard deviation of 2.4 minutes. (a) What is the probability that the…