Math 227
Spring 2009
Section 0147
Mc Gann
Computer assignment #4
1.
The Standard Normal Distribution:
(Remember: mean = 0, and standard deviation = 1)
a)
b)
c)
Find the area to the left of z = 2.13.
Find the area to the right of z = -1.88
Find the z-value for a cumulative probability of 0.8729
Note: Mintab determines a cumulative area by looking at the area to the left of the zvalue. It does not follow our textbook. (See page 300 of textbook)
2.
Checking Data for Normality(See page 315)
The data shown represents the box office total revenue (in millions of dollars) for a
randomly selected sample of top grossing films in 2001. Check for normality.
3.
294
79
53
241
71
51
130
67
144
67
113
56
70
180
97
199
94
165
a)
b)
c)
Construct a histogram to determine normality.
Check for outliers to determine normality.
Calculate Pearson’s Index of skewness.
91
114
202
60
74
56
Central Limit Theorem:
The average age of a vehicle in the United States is 8 years (96 months).
Assume the standard deviation is 16 months. If a random sample of 36
vehicles is selected, find the probability that the mean of a sample is
between 90 and 100 months.
Procedure:
Step 1: You need to find the area in the normal distribution between 90 and 100 if the
mean is 96 and the standard error of the mean is 16 divided by the square root of 36.
Step 2: Calculate and store the standard error of the mean. Select Calc>Calculator.
Store results in K1. For Expression: enter 16/sqrt(36) and click OK
Step 3: Calculate the probability (find the area).
Select Calc>Probability Distributions>Normal. Select options for Cumulative
probability. Enter 96 for the mean. Enter K1 for the standard deviation. Enter 90 for input
constant. Type K2 for Optional storage.
Step 4: Repeat step 3 but change the input constant to 100 and the Optional storage to K3.
Step 5: Well you figure out how to finish it. You will need to use Calc>calculator.