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The Normal Probability Distribution
Quiz

1 .       Consider the uniform density function f(x) = 0.1 for 10 le.gif x le.gif 20. The mean of this distribution is 15 and the standard deviation is about 2.89. Find the probability that x falls between 12 and 15. [Hint]



2 .       Steve conducts an experiment in which he fills up the gas tank on his Chevy Cavalier 40 times and records the average miles per gallon for each fill-up. A histogram of the average miles per gallon indicates the variable is normally distributed with mean of 24.6 miles per gallon and a standard deviation of 3.2 miles per gallon. The area under the curve to the left of X = 26 is 0.6691. How can this area be interpreted? [Hint]



3 .       What is the area under the standard normal curve to the left of z = 1.54? [Hint]



4 .       What is the area under the standard normal curve to the right of z = –1.75? [Hint]



5 .       What is the area under the standard normal curve between z = –0.44 and z = 1.18? [Hint]



6 .       Find the number z such that the proportion of observations that are less than z in a standard normal distribution is 0.8. [Hint]



7 .       Find the number z such that 35% of all observations from a standard normal distribution are greater than z. [Hint]



8 .       What are the z-scores that separate the middle 60% of the data from the area in the tails of the distribution? [Hint]



9 .       Find the value of z0.4. [Hint]



10 .       The length of human pregnancies from conception to birth varies according to a distribution that is approximately normal with mean 266 days and standard deviation 16 days.

What percent of pregnancies last less than 240 days? [Hint]



11 .       Refer back to question ten. What percent of pregnancies last between 240 and 270 days? [Hint]



12 .       A survey was conducted to measure the height of U.S. males. In the survey, respondents were grouped by age. In the 20-29 age group, the heights were normally distributed, with a mean of 69.2 inches and a standard deviation of 2.9 inches. A study participant is randomly selected. (Source: U.S. National Center for Health Statistics)

Find the probability that his height is more than 72 inches. [Hint]



13 .       Refer back to question twelve. Find the probability that his height is between 66 and 72 inches. [Hint]



14 .       The annual per capita use of oranges (in pounds) in the United States can be approximated by a normal distribution with mean 14.9 pounds and standard deviation of 3 pounds. (Source: U.S. Department of Agriculture) What annual per capita consumption of oranges represents the 5th percentile? [Hint]



15 .       The time spent (in days) waiting for a heart transplant in Ohio and Michigan for patients with Type A+ blood can be approximated by a normal distribution with mean 127 days and standard deviation of 23.5 days. (Source: Organ Procurement and Transplant Network) What is the shortest time spent waiting for a heart transplant that would still place a patient in the top 30% of waiting times? [Hint]



16 .       A normal probability plot displays which of the following? [Hint]



17 .       If sample data is taken from a population that is normally distributed, a normal probability plot can be described as which of the following? [Hint]



18 .       Using a normal probability plot, could the following sample data have come from a population that is normally distributed?

ModelMPG
Acura SLX19
Chevrolet Blazer20
Chevrolet Tahoe19
Dodge Durango17
Ford Expedition18
Ford Explorer19
Honda Passport20
Infiniti QX419
Isuzu Trooper19
Jeep Grand Cherokee18
Jeep Wrangler19
Land Rover16
Mazda MPV19
Mercedes-Benz ML32021
Mitsubishi Montero20
Nissan Pathfinder19
Suzuki Sidekick26
Toyota RAV426
Toyota 4Runner22
Source: U.S. Department of Energy, Model Year 1988 Fuel Economy Guide [Hint]



19 .       Fifty-two percent of adults say chocolate chip is their favorite cookie. Forty adults are randomly selected and ask each if chocolate chip is his or her favorite cookie. (Source: WEAREVER)

Approximate the probability that at most 15 people say chocolate chip is their favorite cookie. [Hint]



20 .       Refer back to question four. Approximate the probability that at least 15 people say chocolate chip is their favorite cookie. [Hint]



21 .       Refer back to question four. Approximate the probability that more than 15 people say chocolate chip is their favorite cookie. [Hint]



22 .       Refer back to question four. A community bake sale has prepared 350 chocolate chip cookies. If the bake sale attracts 650 customers and they each buy one cookie, approximate the probability there will not be enough chocolate chip cookies. [Hint]



23 .       The per capita consumption of red meat by people in the U.S. in a recent year was normally distributed, with mean of 115.6 pounds and a standard deviation of 38.5 pounds. Random sample of size 20 are drawn from this population and the mean of each sample is determined. (Source: U.S. Department of Agriculture)

What is the mean of this sampling distribution? [Hint]



24 .       Refer back to question eight. What is the standard deviation of this sampling distribution? [Hint]



25 .       What happens to the mean and to the standard deviation of the distribution of the sample means as the size of the sample increases? [Hint]



26 .       The population mean annual salary for registered nurses is $33,000. A sample of 35 registered nurses is randomly selected. What is the probability that the mean annual salary of the sample is less than $29,500? Assume the standard deviation of the population is $1700. (Source: Jobs Rated Almanac) [Hint]



27 .       During a certain week the mean price of gasoline in California was $1.722 per gallon. A random sample of 38 gas stations is drawn from this population. What is the probability that the mean price for the sample was between $1.727 and 1.737? Assume the standard deviation of the population is $0.049. (Source: Energy Information Administration) [Hint]



28 .       The mean height of women in the U.S. (ages 20-29) is 64 inches. If a random sample of 60 women (ages 20-29) is selected, what is the probability that the mean height for the sample is greater than 66 inches? Assume the standard deviation of the population is 2.75 inches. (Source: National Center for Health Statistics) [Hint]



29 .       A manufacturer claims that the life span of its tires is 50,000 miles. You work for a consumer protection agency and you are testing this manufacturer’s tires. Assume the life spans of the tires are normally distributed. You select 100 tires at random and test them. The mean life span is 49,750 and assume the population standard deviation is 800 miles.

Assuming the manufacturer’s claim is correct, what is the probability the mean of the sample is 49,750 miles or less? [Hint]



30 .       Would it be unusual to have an individual tire with a life span of 49,725 miles? [Hint]



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