Explanation not necessary / required. I would like to check my own responses against those of an expert.

Question 1:

The average American man consumes 9.6 grams of sodium each day. Suppose that the sodium consumption of American men is normally distributed with a standard deviation of 0.8 grams. Suppose an American man is randomly chosen. Let X = the amount of sodium consumed. Round all numeric answers to 4 decimal places where possible.

a) Find the probability that this American man consumes between 9.3 and 10.1 grams of sodium per day.

b) The middle 10% of American men consume between what two weights of sodium? Low? High?

Question 2:

The patient recovery time from a particular surgical procedure is normally distributed with a mean of 3 days and a standard deviation of 1.5 days. Let X be the recovery time for a randomly selected patient. Round all answers to 4 decimal places where possible.

a) What is the probability of spending between 2 and 3 days in recovery?

Question 3:

Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 16 days and a standard deviation of 6 days. Let X be the number of days for a randomly selected trial. Round all answers to 4 decimal places where possible.

a) What is the distribution of X?

b) If one of the trials is randomly chosen, find the probability that it lasted at least 13 days.

c) If one of the trials is randomly chosen, find the probability that it lasted between 19 and 24 days.

d) 81% of all of these types of trials are completed within how many days?

Question 4:

On the planet of Mercury, 4-year-olds average 3.2 hours a day unsupervised. Most of the unsupervised children live in rural areas, considered safe. Suppose that the standard deviation is 1.4 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?

b) Find the probability that the child spends less than 1.5 hours per day unsupervised.

c) What percent of the children spend over 2.4 hours per day unsupervised.

d) 77% of all children spend at least how many hours per day unsupervised?

Question 5:

Americans receive an average of 15 Christmas cards each year. Suppose the number of Christmas cards is normally distributed with a standard deviation of 6. Let X be the number of Christmas cards received by a randomly selected American. Round all answers to 4 decimal places where possible.

a) What is the distribution of X?

b) If an American is randomly chosen, find the probability that this American will receive no more than 13 Christmas cards this year.

c) If an American is randomly chosen, find the probability that this American will receive between 16 and 20 Christmas cards this year.

d) 82% of all Americans receive at most how many Christmas cards? (Please enter a whole number)

Question 6:

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 9. 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?

b) Find the probability that a randomly selected fat calorie percent is more than 38.

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

Question 7:

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 258 feet and a standard deviation of 36 feet. Let X be the distance in feet for a fly ball.

a) What is the distribution of X?

b) Find the probability that a randomly hit fly ball travels less than 302 feet. Round to 4 decimal places.

c) Find the 70th percentile for the distribution of distance of fly balls. Round to 2 decimal places.

Question 8:

According to a study done by UCB students, the height for Martian adult males is normally distributed with an average of 65 inches and a standard deviation of 2.5 inches. Suppose one Martian adult male is randomly chosen. Let X = height of the individual. Round all answers to 4 decimal places where possible.

a) What is the distribution of X?

b) Find the probability that the person is between 65.6 and 69 inches.

c) The middle 20% of Martian heights lie between what two numbers? Low? High?

Question 9:

Los Angeles workers have an average commute of 27 minutes. Suppose the LA commute time is normally distributed with a standard deviation of 15 minutes. Let X represent the commute time for a randomly selected LA worker. Round all answers to 4 decimal places where possible.

a) What is the distribution of X?

b)Find the probability that a randomly selected LA worker has a commute that is longer than 25 minutes.

c) Find the 70th percentile for the commute time of LA workers.

Question 10:

The mean amount of time it takes a kidney stone to pass is 13 days and the standard deviation is 5 days. Suppose that one individual is randomly chosen. Let X = time to pass the kidney stone. Round all answers to 4 decimal places where possible.

a) What is the distribution of X?

b) Find the probability that a randomly selected person with a kidney stone will take longer than 16 days to pass it.

c) Find the minimum number for the upper quarter of the time to pass a kidney stone.

Question 11:

The amount of calories consumed by customers at the Chinese buffet is normally distributed with mean 2888 and standard deviation 684. 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?

b) Find the probability that the customer consumes less than 2695 calories.

c) What proportion of the customers consume over 3199 calories?

d) The Piggy award will given out to the 3% of customers who consume the most calories. What is the fewest number of calories a person must consume to receive the Piggy award?

Question 12:

The average THC content of marijuana sold on the street is 9%. Suppose the THC content is normally distributed with standard deviation of 2%. Let X be the THC content for a randomly selected bag of marijuana that is sold on the street. Round all answers to 4 decimal places where possible,

a) What is the distribution of X?

b) Find the probability that a randomly selected bag of marijuana sold on the street will have a THC content greater than 7.3.

c) Find the 66th percentile for this distribution.