1. 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 1.5 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 2.2 hours per day unsupervised.( )

c.What percent of the children spend over 2.3 hours per day unsupervised.( )% (Round to 2 decimal places)

d.76% of all children spend at least how many hours per day unsupervised? ( )hours.

2. On average, indoor cats live to 15 years old with a standard deviation of 2.3 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 13.8 and 17.1 years old.( )

c.The middle 50% of indoor cats' age of death lies between what two numbers?

Low:( )years

High: ( )years

3. The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard deviation of 11. Suppose that one individual is randomly chosen. Let X=percent of fat calories. Round all answers to 4 decimal places if where possible

a.What is the distribution of X? X ~ N( ),( )

b.Find the probability that a randomly selected fat calorie percent is more than 44.( )

c.Find the minimum number for the lower quarter of percent of fat calories.( )

4. In the 1992 presidential election, Alaska's 40 election districts averaged 2149 votes per district for President Clinton. The standard deviation was 594. (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 2149 a population mean or a sample mean?Select an answer

Population Mean

Sample Mean

c. Find the probability that a randomly selected district had fewer than 2028 votes for President Clinton.( )

d. Find the probability that a randomly selected district had between 2221 and 2445 votes for President Clinton.( )

e. Find the third quartile for votes for President Clinton. Round your answer to the nearest whole number.( )

5. The amount of calories consumed by customers at the Chinese buffet is normally distributed with mean 2966 and standard deviation 527. 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 2644 calories.( )

c. What proportion of the customers consume over 3216 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)

6. The mean height of an adult giraffe is 18 feet. Suppose that the distribution is normally distributed with standard deviation 0.8 feet. Let X be the height of a randomly selected adult giraffe. Round all answers to 4 decimal places where possible.

a. What is the distribution of X? X ~ N( ), ( )

b. What is the median giraffe height? ( )ft.

c. What is the Z-score for a giraffe that is 21 foot tall?( )

d. What is the probability that a randomly selected giraffe will be shorter than 17.5 feet tall?( )

e. What is the probability that a randomly selected giraffe will be between 18.1 and 18.6 feet tall?( )

f. The 90th percentile for the height of giraffes is ( )ft.