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    Statistics: 10 problems

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    Please help with the attached problems 3-80, 3-82, 3-87, 5-34, 5-36, 5-38, 6-45, 6-62, 7-42, 7-45

    80. Creek Ratz is a very popular restaurant located along the coast of northern Florida. They
    serve a variety of steak and seafood dinners. During the summer beach season, they do
    not take reservations or accept "call ahead" seating. Management of the restaurant is
    concerned with the time a patron must wait before being seated for dinner. Listed below
    is the wait time, in minutes, for the 25 tables seated last Saturday night.
    a. Explain why the times are a population.
    b. Find the mean and median of the times.
    c. Find the range and the standard deviation of the times.

    82. The following frequency distribution reports the electricity cost for a sample of 50 two bedroom
    apartments in Albuquerque, New Mexico during the month of May last year.
    a. Estimate the mean cost.
    b. Estimate the standard deviation.
    c. Use the Empirical Rule to estimate the proportion of costs within two standard deviations
    of the mean. What are these limits?

    87. Refer to the Real Estate data, which reports information on homes sold in the Denver,
    Colorado, area last year.
    a. Select the variable selling price.
    1. Find the mean, median, and the standard deviation.
    2. Write a brief summary of the distribution of selling prices.
    b. Select the variable referring to the area of the home in square feet.
    1. Find the mean, median, and the standard deviation.
    2. Write a brief summary of the distribution of the area of homes.

    34. P(A1) = .20, P(A2) = .40, and P(A3) = .40. P(b1|A1) = .25, P(B1|A2) = .05, and P(B1|A3) = .10. Use Bayes Theorem to determine P(A3|B1).

    36. Dr. Stallter has been teaching basic statistics for many years. She knows that 80 percent
    of the students will complete the assigned problems. She has also determined that
    among those who do their assignments, 90 percent will pass the course. Among those
    students who do not do their homework, 60 percent will pass. Mike Fishbaugh took statistics
    last semester from Dr. Stallter and received a passing grade. What is the probability
    that he completed the assignments?

    38. One-fourth of the residents of the Burning Ridge Estates leave their garage doors open when
    they are away from home. The local chief of police estimates that 5 percent of the garages
    with open doors will have something stolen, but only 1 percent of those closed will have
    something stolen. If a garage is robbed, what is the probability the doors were left open?

    45. A Tamiami shearing machine is producing 10 percent defective pieces, which is abnormally
    high. The quality control engineer has been checking the output by almost continuous
    sampling since the abnormal condition began. What is the probability that in a sample of
    10 pieces:
    a. Exactly 5 will be defective?
    b. 5 or more will be defective?

    62. Suppose 1.5 percent of the antennas on new Nokia cell phones are defective. For a random
    sample of 200 antennas, find the probability that:
    a. None of the antennas is defective.
    b. Three or more of the antennas are defective.

    42. The accounting department at Weston Materials, Inc., a national manufacturer of unattached
    garages, reports that it takes two construction workers a mean of 32 hours and
    a standard deviation of 2 hours to erect the Red Barn model. Assume the assembly times
    follow the normal distribution.
    a. Determine the z values for 29 and 34 hours. What percent of the garages take between
    32 hours and 34 hours to erect?
    b. What percent of the garages take between 29 hours and 34 hours to erect?
    c. What percent of the garages take 28.7 hours or less to erect?

    45. Shaver Manufacturing, Inc., offers dental insurance to its employees. A recent study by the
    human resource director shows the annual cost per employee per year followed the normal
    probability distribution, with a mean of $1,280 and a standard deviation of $420 per year.
    a. What fraction of the employees cost more than $1,500 per year for dental expenses?
    b. What fraction of the employees cost between $1,500 and $2,000 per year?
    c. Estimate the percent that did not have any dental expense.
    d. What was the cost for the 10 percent of employees who incurred the highest dental

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