1. The amount of calories consumed by customers at the Chinese buffet is normally distributed with mean 2744 and standard deviation 558. One randomly selected customer is observed to see how many calories X that customer consumes. Round all answers to 4 decimal places where possible.
a. What is the distribution of X? X ~ N(,)
b. Find the probability that the customer consumes less than 2546 calories.
c. What proportion of the customers consume over 3082 calories?
d. The Piggy award will given out to the 1% of customers who consume the most calories. What is the fewest number of calories a person must consume to receive the Piggy award? calories. (Round to the nearest calorie)
2. On average, indoor cats live to 12 years old with a standard deviation of 2.2 years. Suppose that the distribution is normal. Let X = the age at death of a randomly selected indoor cat. Round answers to 4 decimal places where possible.
a. What is the distribution of X? X ~ N(,)
b. Find the probability that an indoor cat dies when it is between 8.9 and 12.9 years old.
c. The middle 50% of indoor cats’ age of death lies between what two numbers?
Low: years
High: years
3. On the planet of Mercury, 4-year-olds average 2.8 hours a day unsupervised. Most of the unsupervised children live in rural areas, considered safe. Suppose that the standard deviation is 1.3 hours and the amount of time spent alone is normally distributed. We randomly survey one Mercurian 4-year-old living in a rural area. We are interested in the amount of time X the child spends alone per day. (Source: San Jose Mercury News) Round all answers to 4 decimal places where possible.
a. What is the distribution of X? X ~ N(,)
b. Find the probability that the child spends less than 1.7 hours per day unsupervised.
c. What percent of the children spend over 3.2 hours per day unsupervised. % (Round to 2 decimal places)
d. 87% of all children spend at least how many hours per day unsupervised? hours.
4. In the 1992 presidential election, Alaska’s 40 election districts averaged 2169 votes per district for President Clinton. The standard deviation was 583. (There are only 40 election districts in Alaska.) The distribution of the votes per district for President Clinton was bell-shaped. Let X = number of votes for President Clinton for an election district. (Source: The World Almanac and Book of Facts) Round all answers except part e. to 4 decimal places.
a. What is the distribution of X? X ~ N(,)
b. Is 2169 a population mean or a sample mean? Select an answer Sample Mean Population Mean
c. Find the probability that a randomly selected district had fewer than 2109 votes for President Clinton.
d. Find the probability that a randomly selected district had between 2304 and 2508 votes for President Clinton.
e. Find the first quartile for votes for President Clinton. Round your answer to the nearest whole number.
5. Suppose that the speed at which cars go on the freeway is normally distributed with mean 75 mph and standard deviation 5 miles per hour. Let X be the speed for a randomly selected car. Round all answers to 4 decimal places where possible.
a. What is the distribution of X? X ~ N(,)
b. If one car is randomly chosen, find the probability that it is traveling more than 73 mph.
c. If one of the cars is randomly chosen, find the probability that it is traveling between 74 and 78 mph.
d. 90% of all cars travel at least how fast on the freeway? mph.
6. Suppose that the speed at which cars go on the freeway is normally distributed with mean 75 mph and standard deviation 5 miles per hour. Let X be the speed for a randomly selected car. Round all answers to 4 decimal places where possible.
a. What is the distribution of X? X ~ N(,)
b. If one car is randomly chosen, find the probability that it is traveling more than 73 mph.
c. If one of the cars is randomly chosen, find the probability that it is traveling between 74 and 78 mph.
d. 90% of all cars travel at least how fast on the freeway? mph.
