PROBLEM 8 (15 points) Empirical Rule

1)Based on a survey, annual salaries for benefits managers range from $50,935 to $79,577. A sample of 30 benefit managers salaries were taken and the mean of the data was $63,000 with a sample standard deviation of $4,000. Assume that the distribution of the annual salaries is bell-shaped and assumes a normal distribution.

a. Determine the percentage of annual salaries between $51,000 and $67,000 using the empirical rule

b. Determine the percentage of annual salaries less than $55,000 using the empirical rule.

c. Determine the percentage of annual salaries that earned more than $75,000 using the empirical rule.

2)An airline has determined that 20% of its international flights are not on time. Use the normal approximation to the binomial distribution to answer the following questions. What is the probability that of the next 80 international flights

a.

Less than 16 will not be on time?

b.

More than 17 will not be on time?

c.

Exactly 17 will not be on time?

3)The prices of condos in a city are normally distributed with a mean of $90,000 and a standard deviation of $28,000.

a.

The city government exempts the cheapest 6.68% of the condos from city taxes. What is the maximum price of the condos that will be exempt from city taxes?

b.

If 1.79% of the most expensive condos are subject to a luxury tax, what is the minimum price of condos that will be subject to the luxury tax?