6 4 Applications of the Standard Normal Distribution

6. 4: Applications of the Standard Normal Distribution By the end of class you will be able to solve real world problems using the normal distribution and determine if a distribution is normal.

The average admission charge for amusement parks is normally distributed with a mean of $45 and standard deviation of $6. 50. Find the probability that an amusement park ticket is less than $40.

Method 1: Convert to z value Use the formula to convert variable to z value Use normal. CDF (low, high, z)

Method 2: No Conversion Use norm. CDF (low, high, mean, st. dev)

The winnings of Wheel of Fortune contestants are normally distributed with a mean of $16, 000 and a standard deviation of $2, 100

Calculate the following P(X<$15, 000) P(X>$19, 000) P($9, 000<X<$24, 500)

The average length of a hospital stay is 5. 9 days. If we assume a normal distribution and a standard deviation of 1. 7 days, 15% of hospital stays are less than how many days?

Finding Variable Values Use inv. NORM( area to left, mean, st. dev)

The average person is willing to spend $6, 000 on a used car. He wants to sell cars that appeal to the middle 70% of the population. The distribution is normally distributed with a standard deviation of $500. Find the minimum and maximum prices of a car that the dealer will sell.

The following data represents the number of runs scored by a baseball player each year of his career. Check for normailty. 30 59 69 50 58 71 55 43 66 52 56 62 36 13 29 17 3

Tests for Normality Construct a frequency distribution and histogram (bell curve) Use Pearson’s Index: (s = standard deviation) Check for outliers using IQR (Q 1— 1. 5 IQR, Q 3+1. 5 IQR)

A survey of grocery stores showed how many days’ inventory the stores had. Check for normality. 5 29 81 34 88 44 91 151 45 97 63 98 158 68 74 74 113 118