1. 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.

2. 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.
.2209

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

4. Method 2: No Conversion
Use normCDF (low, high, mean, st. dev)

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

6. Calculate the following
P(X<$15,000)
P(X>$19,000)
P($9,000<X<$24,500)
1) .1169, 2) 0, 3) .0764

7. The average length of a hospital stay is 5. 9 days
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?
4.13

8. Finding Variable Values
Use invNORM( area to left, mean, st. dev)

9. The average person is willing to spend $6,000 on a used car
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.
5481, 6518

10. The following data represents the number of runs scored by a baseball player each year of his career. Check for normailty
Create a frequency table and histogram with students, mean = 45.24, median = 52, s = 20.58, Q1 29.5, Q3 60.5, PI (-.985), Quartile Check: IQR = 31, Q1-1.5(IQR) = -17, Q3+1.5(IQR) = 107

11. Tests for Normality
Construct a frequency distribution and histogram (bell curve)
Use Pearson’s Index: (s = standard deviation)
Check for outliers using IQR (Q1—1.5IQR, Q3+1.5IQR)

12. A survey of grocery stores showed how many days’ inventory the stores had. Check for normality
See book pg 313. Have different rows do different tests.