Week 7: Homework Assignment

Homework 4

Show your PhStat output or COMPLETE calculations to receive full points.

Question 1. Given a standardized normal distribution (with a mean of 0 and a standard deviation of 1), what is the probability that:

1. Z is less than 1.67

1. Z is greater than 1.95

1. Z is between 1.67 and 1.95

1. Z is less than 1.67 or greater than 1.95

1. What is the value of Z if only 15 percent of all possible Z values are larger?

1. Between what two values of Z (symmetrically distributed around the mean) will 68.26 percent of all possible Z values be contained?

Question 2. Given a normal distribution with m = 90 and s = 15, what is the probability that:

1. X > 85?

1. X < 65?

1. X < 75 or X > 85?

1. Between what two X values (symmetrically distributed around the mean) are 90 percent of the values?

Question 3. Given a normal distribution with m = 60 and s = 8, what is the probability that:

1. 15% of the values are less than what X value?

1. Between what two X values (symmetrically distributed around the mean) are ninety percent of the values?

Question 4. In 2014, the per capital consumption of bottled water in the United States was reported to be 35 gallons. Assume that the per capital consumption of bottled water in the United States is approximately normally distributed with a mean of 40 gallons and a standard deviation of 10 gallons.

1. What is the probability that someone in the United States consumed between 8 and 20 gallons of bottled water in 2014?

1. What is the probability that someone in the United States consumed less than 9 gallons of bottled water in 2014?

1. Ninety percent of the people in the United States consumed less than how many gallons of bottled water.