Reference no: EM132844697

Continuous Distributions

1. The duration of long-distance calls made by employees of a company are normally distributed with a mean of 6.3 minutes and a standard deviation of 2.2 minutes. Find the probability that a call

a. lasts between 5 and 10 minutes

b. lasts more than 7 minutes

c. lasts less than 4 minutes

d. How long do the longest 10% of the calls last?

2. The heights of children 2 years old are normally distributed with a mean of 32 inches and a standard deviation of 1.5 inches. Pediatricians regularly measure the heights of toddlers to determine whether there is a problem. There may be a problem when a child is in the top or bottom 5% of heights.

a. Determine the heights of 2 year-old children that could be a problem.

b. Find the probability a 2 year old child is taller than 36 inches.

c. Find the probability a 2 year old child is shorter than 34 inches.

d. Find the probability a 2 year old child is between 30 and 33 inches tall.

3. Because of relatively high interest rates, most consumers attempt to pay off their credit card bills promptly. However, this is not always possible. An analysis of the amount of interest paid monthly by a bank's Visa card holders reveals the amount is normally distributed with a mean of $27 and a standard deviation of $7.

a. What proportion of the bank's Visa cardholders pay more than $30 in interest?

b. What proportion of the bank's Visa cardholders pay more than $40 in interest?

c. What proportion of the bank's Visa cardholders pay less than $15 in interest?

d. What interest payment is exceeded by only 20% of the bank's Visa cardholders?

4. How much money does a typical family of four spend at McDonald's restaurants per visit? The amount is a normally distributed random variable whose mean is $16.40 and whose standard deviation is $2.75.

a. Find the probability a family of four spends less than $10.

b. What is the amount below which only 10% of families of four spend at McDonald's?

5. The final grades in a statistics course are normally distributed with a mean of 70 and a standard deviation of 10. The professor must convert all numeric grades to letter grades. She decides she want 10% A's, 30% B's, 40% C's, 15% D's, and 5% F's. Determine the cutoffs for each letter grade.