5.9 Determine the following:
a. For n = 4 and p = 0.12, what is P1X = 02?
b. For n = 10 and p = 0.40, what is P1X = 92?
c. For n = 10 and p = 0.50, what is P1X = 82?
d. For n = 6 and p = 0.83, what is P1X = 52?
5.12 A recent Pew Research survey reported that 48% of 18- to 29-year-olds in the United States own tablets. Using the binomial distribution, what is the probability that in the next six 18- to 29-year-olds surveyed:
a. four will own a tablet?
b. all six will own a tablet?
c. at least four will own a tablet?
d. What are the mean and standard deviation of the number of 18- to 29-year olds who will own a tablet in a survey of six?
e. What assumptions do you need to make in (a) through (c)?
5.14 A manufacturing company regularly conducts quality control checks at specified periods on the products it manufactures. Historically, the failure rate for LED light bulbs that the company manufactures is 5%. Suppose a random sample of 10 LED light bulbs is selected. What is the probability that:
a. none of the LED light bulbs are defective?
b. exactly one of the LED light bulbs is defective?
c. two or fewer of the LED light bulbs are defective?
d. three or more of the LED light bulbs are defective?
5.18 Assume a Poisson distribution.
a. If l = 2.5, find P1X = 22.
b. If l = 8.0, find P1X = 82.
c. If l = 0.5, find P1X = 12.
d. If l = 3.7, find P1X = 02.
5.21 Assume that the number of new visitors to a website in one hour is distributed as a Poisson variable. The mean number of new visitors to the website is 4.0 per hour. What is the probability that in any given hour:
a. zero new visitors will arrive at the website?
b. exactly one new visitor will arrive at the website?
c. two or more new visitors will arrive at the website?
d. fewer than three new visitors will arrive at the website?
5.27 J.D. Power and Associates calculates and publishes various statistics concerning car quality. The dependability score measures problems experienced during the past 12 months by original owners of three-year-old vehicles (those that were introduced for the 2010 model year). For these models of cars, Ford had 1.27 problems per car and Toyota had 1.12 problems per car. Let X be equal to the number of problems with a three-year old Ford.
a. What assumptions must be made in order for X to be distributed as a Poisson random variable? Are these assumptions reasonable?
Making the assumptions as in (a), if you purchased a Ford in the 2010 model year, what is the probability that in the past 12 months, the car had:
b. zero problems?
c. two or fewer problems?
d. Give an operational definition for problem. Why is the operational definition important in interpreting the initial quality score?
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