The mean amount of money that a family of four will spend at Kings Island, including the food and souvenirs, is $130 with a standard deviation of $12.Assume that this distribution is normal and calculate the following:

Find the probability that a particular family of four selected at random spends between $150 and $200?

What is the probability that the family spends less than $140?

What is the probability that the family spends more than $170?

What is the probability that the family spends between $130 and $190? (Be able to draw a graph to illustrate your results.)

Find the cost that represents the 50^th percentile.

Find the cost that represents the 90^th percentile.

5% of the families spend below what value?

The top 5% of the families spend above what value?

Between which two values will the middle 50% of the families spend?

What percent of the families spend at least $120?

Use the empirical rule to determine the following:

AAbout 68% of the observations lie between which two values?

BAbout 95% of the observations lie between which two values?

CAbout 99% of the observations lie between which two values?

Use the normal distribution to determine the following:

A68% of the observations lie between which two values?

B95% of the observations lie between which two values?

C99% of the observations lie between which two values?

Discuss the differences in the results for question 12 and question 11.