All answers need to be typed and show your work including formula for full credit. Use calculator to be ready for midterm exam. (25 points total)

1. Suppose Z shows a standard normal distribution with mean 0 and standard deviation of 1. Find the probability of following ranges. (1 point each)

1)P(Z > 0.5) =

2)P(Z > -2) =

3)P(-1 < Z < 2) =

4)P( Z < 2.5) =

5)P(Z > 1.2) =

2.Morgan trucking company determined that on an annual basis the distance traveled per truck is normally distributed with a mean of 50 thousand miles and standard deviation of 12 thousand miles. (Use the standard normal distribution table from the textbook) (2 points each)

1)What the probability that a truck travels less than 34 thousand miles per year?

2)What is the probability that a truck travels between 34 and 50 thousand miles per year?

3)What is the probability that a truck travel more than 70 thousand miles per year?

3. In 2014, the per capita consumption of soft drinks in the United States was reported to be 42.1 gallons. Assume that the per capita consumption of soft drinks in the United States is approximately normally distributed with a mean of 42.1 gallons and a standard deviation of 13 gallons. (Use the standard normal distribution table from the textbook) (2 points each)

1)What is the probability that someone in the United States consumed more than 60 gallons of soft drinks in 2014?

2)What is the probability that someone in the United States consumed between 15 and 30 gallons of soft drinks in 2014?

3)Ninety-five percent of the people in the United States consumed less than how many gallons of soft drinks?