# Andre is a fearless circus performer who gets shot from a special

7.34 Andre is a fearless circus performer who gets shot from a special cannon during the grand finale of the show and is supposed to land on a safety net at the other side of the arena. The distance he travels varies, but is normally distributed with a mean of 150 feet and a standard deviation of 10 feet. The landing net is 30 feet long.

Please round (b) to 4 decimal places.

a. To maximize Andre’s probability of landing on the net, how far away from the cannon should he position the nearest edge of the net?
[removed][removed].

b. Given the net position in part (a), what is the probability that Andre will be able to return for tomorrow night’s show?
[removed][removed].

A company sells toothpaste in a tube advertised to contain 8 ounces. The tube filling process is set with a mean of 8.17 ounces. In this continuous production process, the amount of toothpaste put in a tube is normally distributed with a mean of 8.17 ounces and a standard deviation of 0.12 ounces. If the actual capacity of the tubes used is 8.49 ounces, what proportion of the tubes will be filled beyond capacity?

P = [removed][removed]

7.14 The average American family of four spends \$5000 per year on food prepared at home. Assuming a normal distribution with a standard deviation of \$1000 and a randomly selected American family of four, the probability that the family’s annual spending for food prepared at home will be. (SOURCE: “Business Briefing,” Pittsburgh Tribune-Review, July 5, 2009, p. E1.)

a. more than \$8000 is [removed][removed]

b. between \$5000 and \$7000 is [removed][removed]

c. less than \$6000 is [removed][removed]

d. between \$3000 and \$6000 is [removed][removed]

7.6 In the normal distribution, the probability that x will exceed (+2) is the same as the probability that x will be less than (-2). What characteristic of the normal distribution does this reflect?

Symmetry

Skew

Correlation

Determine P(z>=1.71) for the standard normal curve.

P(z>=1.71) = [removed][removed]

7.36 KleerCo supplies an under-hood, emissions-control air pump to the automotive industry. The pump is vacuum powered and works while the engine is operating, cleaning the exhaust by pumping extra oxygen into the exhaust system. If a pump fails before the vehicle in which it is installed has covered 50,000 miles, federal emissions regulations require that it be replaced at no cost to the vehicle owner. The company’s current air pump lasts an average of 63,000 miles, with a standard deviation of 10,000 miles. The number of miles a pump operates before becoming ineffective has been found to be normally distributed.

Please round (a) and (c) to 4 decimal places.

a. For the current pump design, the percentage of the company’s pumps that will have to be replaced at no charge to the consumer is [removed][removed]. (be sure to express your answer as a decimal)

b. The percentage of the company’s pumps that will fail at exactly 50,000 miles is [removed][removed].

c. The percentage of the company’s pumps that will fail between 40,000 and 55,000 miles is [removed][removed]. (be sure to express your answer as a decimal)

d. If the number of miles is [removed][removed]or greater than the probability is 80% that a randomly selected pump will no longer be effective.

7.10 The Canada Urban Transit Association has reported that the average revenue per passenger trip during a given year was \$1.55. If we assume a normal distribution and a standard deviation of = \$0.20. (SOURCE: American Public Transit Association, APTA 2009 Transit Fact Book, p. 35.)

Please round (a) to 1 decimal, and (b) through (d) to 3 decimals.

a. The proportion of passenger trips that produced revenue of less than \$1.55 is [removed][removed].

b. The proportion of passenger trips that produced revenue of between \$1.15 and \$1.95 is [removed][removed].

c. The proportion of passenger trips that produced revenue of between \$1.35 and \$1.75 is [removed][removed].

d. The proportion of passenger trips that produced revenue of between \$0.95 and \$1.55 is [removed][removed]

7.32 In 2009, the average charge for tax preparation by H&R Block, Inc. was \$187. Assuming a normal distribution and a standard deviation of = \$20. (SOURCE: Source: hrblock.com, July 14, 2009.) The tax preparation fee that would have been exceeded by 90% of the tax preparation customers is \$[removed][removed] .

7.24 Using the standard normal table, determine a z value such that the:

a. Cumulative area to z is 0.7486. z = [removed][removed]

b. Cumulative area to z is 0.0735. z = [removed][removed]

c. Area between z and positive infinity is 0.3508. z = [removed][removed]

d. Area between z and positive infinity is 0.0212. z = [removed][removed]

7.4 The probability that a continuous random variable will take on any specific value is [removed]

Assume x is normally distributed with mean = 14 and standard deviation = 5. Use the approximate areas beneath the normal curve, as discussed in this section, to find P(9 <=x<=19).

[removed][removed]

7.20 Using the standard normal table, find the following probabilities associated with z:

a. P(0.00 ≤ z ≤ 1.25) = [removed][removed]

b. P(-1.25 ≤ z ≤ 0.00) = [removed][removed]

c. P(-1.25 ≤ z ≤ 1.25) = [removed][removed]

7.18 A continuous random variable, x, is normally distributed with a mean of \$1000 and a standard deviation of \$100. Convert each of the following x values into its corresponding z-score:

a. x = \$1000. [removed][removed]

b. x = \$750. [removed][removed]

c. x = \$1100. [removed][removed]

d. x = \$950. [removed][removed]

e. x = \$1225. [removed][removed]

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