# MATHEMATICS

Must show all work. Excel files to do work on are attached.

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?

5.15 Past records indicate that the probability of online retail or-ders that turn out to be fraudulent is 0.08. Suppose that, on a given day, 20 online retail orders are placed. Assume that the number of online retail orders that turn out to be fraudulent is distributed as a binomial random variable.

a. What are the mean and standard deviation of the number of on-line retail orders that turn out to be fraudulent?

b. What is the probability that zero online retail orders will turn out to be fraudulent?

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?

5.25 The U.S. Department of Transportation maintains statis-tics for involuntary denial of boarding. In July–September 2013, the American Airlines rate of involuntarily denying boarding was 0.45 per 10,000 passengers. What is the probability that in the next 10,000 passengers, there will be

a. no one involuntarily denied boarding?

b. at least one person involuntarily denied boarding?

c. at least two persons involuntarily denied boarding?

6.1 Given a standardized normal distribution (with a mean of 0 and a standard deviation of 1, as in Table E.2), what is the probability that

a. Z is less than 1.57?

b. Z is greater than 1.84?

c. Z is between 1.57 and 1.84?

d. Z is less than 1.57 or greater than 1.84?

6.5 Given a normal distribution with m=100 and s=10, what is the probability that

a. X 775?

b. X 670 ?

c. X 680 or X 7110 ?

d. Between what two X values (symmetrically distributed around the mean) are eighty percent of the values?

6.7 According to the “Bottled Water Trends for 2014” report (bit .ly/1gx5ub8), the U.S. per capita consumption of bottled water in 2013 was 31.8 gallons. Assume that the per capita consumption of bottled water in the United States is approximately normally distributed with a mean of 31.8 gallons and a standard deviation of 10 gallons.

a. What is the probability that someone in the United States con-sumed more than 32 gallons of bottled water in 2013?

b. What is the probability that someone in the United States consumed between 10 and 20 gallons of bottled water in 2013?

c. What is the probability that someone in the United States consumed less than 10 gallons of bottled water in 2013?

d. Ninety-nine percent of the people in the United States consumed less than how many gallons of bottled water?

6.9 Consumers spent an average of $14.99 on a meal at a restau-rant in 2013. (Data extracted from bit.ly/1hObH22.) Assume that the amount spent on a restaurant meal is normally distributed and that the standard deviation is $2.

a. What is the probability that a randomly selected person spent more than $15?

b. What is the probability that a randomly selected person spent between $10 and $12?

c. Between what two values will the middle Ninety-five percent of the amounts spent fall?

6.11 A Nielsen study indicates that 18- to 24- year olds spend a mean of 135 minutes watching video on their smartphones per month. (Data extracted bit.ly/1hF3BP2.) Assume that the amount of time watching video on a smartphone per month is normally distrib-uted and that the standard deviation is 15 minutes.

a. What is the probability that an 18- to 24-year-old spends less than 112 minutes watching video on his or her smartphone per month?

b. What is the probability that an 18- to 24-year-old spends be-tween 112 and 158 minutes watching video on his or her smart-phone per month?

c. What is the probability that an 18- to 24-year-old spends more than 158 minutes watching video on his or her smartphone per month?

d. One percent of all 18- to 24-year-olds will spend less than how many minutes watching video on his or her smartphone per month?