4.2 What is the probability that a standard normal random variable will be between the values -2 and 1?

4.6 Find the probability that a standard normal random variable will have a value less than or equal to -2.5.

4.14 Find a value such that that the probability that the standard normal random variable will be above it is 0.85.

4.28 The time it takes an international telephone operator to place an overseas phone call is normally distributed with mean 45 seconds and standard deviation 10 seconds.

1. What is the probability that my call will go through in less than 1 minute?
2. What is the probability that I will get through in less than 40 seconds?
3. What is the probability that I will have to wait more than 70 seconds for my call to go through?

4.52 The manager of a restaurant knows from experience that 70% of the people who make reservations for the evening show up for dinner. The manager decides one evening to overbook and accept 20 reservations when only 15 tables are available. What is the probability that more than 15 parties will show up?

5.2 An auditor selected a random sample of 12 accounts from all accounts receivable of a given firm. The amounts of the accounts, in dollars, are as follows: 87.50, 123.10, 45.30, 52.22, 213.00, 155.00, 39.00, 76.05, 49.80, 99.99, 132.00, 102.11. Compute an estimate of the mean amount of all accounts receivable. Give an estimate of the variance of all the amounts.

5.6 A market research worker interviewed a random sample of 18 people about their use of a certain product. The results, in terms of Y or N (for yes, a user of the product, or No, not a user of the product), are as follows: Y N N Y Y Y N Y N Y Y Y N Y N Y Y N. Estimate the population proportion of users of the product.

5.14 What is the most significant aspect of the central limit theorem?

5.22 An economist wishes to estimate the average family income in a certain population. The population standard deviation is known to be $4,500, and the economist uses a random sample of size n = 225. What is the probability that the sample mean will fall within $800 of the population mean?

5.26 It has been suggested that an investment portfolio selected randomly by throwing darts at the stock market page of The Wall Street Journal may be a sound (and certainly well-diversified) investment. Suppose that you own such a portfolio of 16 stocks randomly selected from all stocks listed on the New York Stock Exchange (NYSE). On a certain day, you hear on the news that the average stock on the NYSE rose 1.5 points. Assuming that the standard deviation of stock price movements that day was 2 points and assuming stock price movements were normally distributed around their mean of 1.5, what is the probability that the average stock price of your portfolio increased?

1. The random samples of sizes, 30, 48, and 32 respectively, are collected, and the three sample means are computed. What is the total number of degrees of freedom for deviations from the means?

1. Your bank sends you a summary statement, giving the average amount of all checks you wrote during the month. You have a good record of the amounts of 17 out of the 19 checks you wrote during the month. Using this and the information provided by the bank, can you figure out the amounts of the two missing checks? Explain.

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