Question

1. A continuous random variable is normally distributed. The probability that a value in the distribution is greater than 47 is 0.4004. Find the probability that a value in the distribution is less than 47.

2. A continuous random variable is normally distributed. The probability that a value in the distribution is less than 125 is 0.5569. Find the probability that a value in the distribution is greater than 125.

3. A random variable is normally distributed with mean 89.7 and standard deviation 17.4. What value is 3 standard deviations below the mean?

4. The amount of soda in a randomly selected bottle varies according to a normal distribution with mean 16 ounces and standard deviation 9.2 ounces. What is the probability that a randomly selected bottle will be less than 16 ounces? Enter your answer as a decimal.

5.  A random variable is normally distributed with mean 85.9 and standard deviation 9.2. What value is 2 standard deviations above the mean?

Answer 1

Question 1

probability that a value in the distribution is greater than 47 is 0.4004

Probability that a value is the distribution is less than 47 = 1 - 0.4004 = 0.5996

Question 2

probability that a value in the distribution is less than 125 is 0.5569.

probability that a value in the distribution is greater than 125 = 1 - 0.5569 = 0.4431

Question 3

Mean = 89.7

standard deviation = 17.4

Value that is 3 standard deviations below the mean = 89.7 - 3 * 17.4 = 37.5

Question 4

Mean = 16 ounces

standard deviation = 9.2 ounces

Probability that a randomly selected bottle will be less than 16 ounces = 0.50

Question 5

Mean = 85.9

standard deviation = 9.2

Value is 2 standard deviation above the mean = 85.9 + 9.2 * 2 = 104.3