Cumulative Review 295 13. An auto parts seller finds that 1 in every 200 parts sold is defective. Use the geometric distribution to find the probability that (a) the first defective part is the fifth part sold, (b) the first defective part is the first, second, or third part sold, and (c) none of the first 20 parts sold are defective. 14. The table shows the results of a survey in which 3,545,286 public and 509,168 private school teachers were asked about their full-time teaching experience. (Adapted from National Center for Education Statistics) Public Private Total Less than 3 years 318,274 61,809 380,083 3 to 9 years 1,003,014 151,865 1,154,879 10 to 20 years 1,415,824 167,400 1,583,224 More than 20 years 808,174128,094 936,268 Total 3,545,286 509,168 4,054,454 (a) Find the probability that a randomly selected private school teacher has 10 to 20 years of full-time teaching experience. (b) Find the probability that a randomly selected teacher is at a public school, given that the teacher has 3 to 9 years of full-time experience. (c) Are the events “being a public school teacher” and “having more than 20 years of full-time teaching experience” independent? Explain. (d) Find the probability that a randomly selected teacher has 3 to 9 years of full-time teaching experience or is at a private school. 15. The initial pressures for bicycle tires when first filled are normally distributed, with a mean of 70 pounds per square inch (psi) and a standard deviation of 1.2 psi. (a) Random samples of size 40 are drawn from this population, and the mean of each sample is determined. Find the mean and standard deviation of the sampling distribution of sample means. Then sketch a graph of the sampling distribution. (b) A random sample of 15 tires is drawn from this population. What is the probability that the mean tire pressure of the sample is less than 69 psi? 16. The life spans of car batteries are normally distributed, with a mean of 44 months and a standard deviation of 5 months. (a) Find the probability that the life span of a randomly selected battery is less than 36 months. (b) Find the probability that the life span of a randomly selected battery is between 42 and 60 months. (c) What is the shortest life expectancy a car battery can have and still be in the top 5% of life expectancies? 17. A florist has 12 different flowers from which floral arrangements can be made. A centerpiece is made using four different flowers. (a) How many different centerpieces can be made? (b) What is the probability that the four flowers in the centerpiece are roses, daisies, hydrangeas, and lilies? 18. Sixty-seven percent of dating U.S. adults say their dating lives are not going well. You randomly select 10 dating U.S. adults. (a) Construct a binomial distribution for the random variable x, the number who say their dating lives are not going well. (b) Graph the binomial distribution using a histogram and describe its shape. (c) Identify any values of the random variable x that you would consider unusual. Explain. (Source: Pew Research Center)
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