Suppose the fire station must call for additional equipment from a neighboring city

a. All 10 automobiles failed the inspection. b. Exactly 6 of the 10 failed the inspection.

c. Six or more failed the inspection. d. All 10 passed the inspection.

Use the following Minitab output to answer the questions. Note that with Minitab, the binomial probability p is denoted by p and the binomial variable y is represented by x. Bus. 4.46 Over a long period of time in a large multinational corporation, 10 of all sales trainees are rated as outstanding, 75 are rated as excellent good, 10 are rated as satisfactory, and 5 are considered unsatisfactory. Find the following probabilities for a sample of 10 trainees selected at random:

a. Two are rated as outstanding. b. Two or more are rated as outstanding.

c. Eight of the ten are rated either outstanding or excellent good. d. None of the trainees is rated as unsatisfactory. Med. 4.47 A relatively new technique, balloon angioplasty, is widely used to open clogged heart valves and vessels. The balloon is inserted via a catheter and is inflated, opening the vessel; thus, no surgery is required. Left untreated, 50 of the people with heart-valve disease die within about 2 years. If experience with this technique suggests that approximately 70 live for more than 2 years, would the next five patients of the patients treated with balloon angioplasty at a hospital constitute a binomial experiment with n ⫽ 5, p ⫽ .70? Why or why not? Bus. 4.48 A random sample of 50 price changes is selected from the many listed for a large super- market during a reporting period. If the probability that a price change is posted correctly is .93, a. Write an expression for the probability that three or fewer changes are posted incorrectly. b. What assumptions were made for part a? 4.49 Suppose the random variable y has a Poisson distribution. Use Table 15 in the Appendix to compute the following probabilities:

a. Py ⫽ 1 given m ⫽ 3.0 b. Py ⬎ 1 given m ⫽ 2.5

c. Py ⬍ 5 given m ⫽ 2.0 4.50 Cars arrive at a toll booth at a rate of six per 10 seconds during rush hours. Let N be the number of cars arriving during any 10-second period during rush hours. Use Table 15 in the Appendix to compute the probability of the following events:

a. No cars arrive. b. More than one car arrives.

c. At least two cars arrive. 4.51 A firm is considering using the Internet to supplement its traditional sales methods. From the data of similar firms, it is estimated that one of every 1,000 Internet hits result in a sale. Sup- pose the firm has 2,500 hits in a single day.

a. Write an expression for the probability that there are less than six sales, do not com-

plete the calculations. b. What assumptions are needed to write the expression in part a? Binomial Distribution with n 10 and p 0.6 x PX x PX x 0.00 0.0001 0.0001 1.00 0.0016 0.0017 2.00 0.0106 0.0123 3.00 0.0425 0.0548 4.00 0.1115 0.1662 5.00 0.2007 0.3669 6.00 0.2508 0.6177 7.00 0.2150 0.8327 8.00 0.1209 0.9536 9.00 0.0403 0.9940 10.00 0.0060 1.0000