1. It is stated that 86% of U.S. respondents use a cell phone exclusively for their telephone service. In a sample of twelve households,
a. Find the probability that fewer than 6 respondents use a cell phone as their exclusive telephone service.
P(X<=5)=0.0004 b. Find the probability that exactly 11 respondents exclusively use a cell phone for telephone service. P(X=11)=0.3197 c. Find the number of respondents would you expect to be exclusively using cell phones. mu=np=10.32 2. Clients facing trouble with their Internet may call a number for support. The time it takes the technician to resolve the problem is equally likely to be between 30 seconds and 8 minutes. a. What are the values for a and b in minutes? (0.5, 8) b. What is the mean time to resolve the problem? What is the standard deviation of the time? 4.25 minutes, 2.17 minutes c. What percent of the problems take more than 7 minutes to resolve? 13% d. Suppose we wish to find the middle 80% of the problem-solving times. What are the end points of these two times? (1.25, 7.25) minutes 3. Google stock was trading for an average of $1018.27 on 2/9/2018. Suppose the value of the stock that day was normally distributed with a standard deviation of $8.57. a. What was the probability that the stock was valued between $1020 and $1060? 0.42 b. Five percent of the time the stock was trading at what value or higher? $1032.37 c. What is the maximum price you should pay if you don’t want to exceed the twentieth percentile of costs? $1011.06 4. A study found the average song in the top 100 on iTunes is 226.93 seconds with a standard deviation of 31.50 seconds. a. What is the probability that a randomly selected song is less than two and a half minutes? 0.0073 b. What percent of songs are longer than the Beatles’ Revolution (3 minutes 21 seconds)? 79% c. In a sample of 16 songs, what is the likelihood that the mean song length is longer than 4 minutes? 0.0485 d. In repeated samples of 16 songs, we’d expect 95% of mean song lengths to be between what two numbers? (211.50, 242.36) seconds