Section 2-2 Review Worksheet
Section 2.2 Normal Calculations Review Name___KEY_____________________
For each question, be sure to draw the appropriate pictures and show the appropriate formulas. Show your work as if this was a quiz or a test.
Doc and Marty spend a full day at Hill Valley Raceway testing some new tires on the DeLorean. For 400 laps, they record the laptime in minutes. At the end of the day, Doc plots the distribution of times and realizes that it follows an approximately Normal distribution with a mean of 1.84 and a standard deviation of .07.
1. Doc would really like the laptimes to be consistently between 1.75 and 1.85 minutes. What proportion of his laps were in this range? Interpret your result in the context of the problem.
Use normalcdf ( 1.75, 1.85, 1.84, 0.07 )
Doc and Marty should have laptimes between 1.75 and 1.85 approximately 45.75% of the time.
2. In order to beat Biff in an upcoming street race, Marty needs to have lap times that are less than 1.72 minutes. Find the proportion of laps that were faster than 1.72 minutes. Interpret your result in the context of the problem.
Use normalcdf ( -999999, 1.72, 1.84, 0.07 )
About 4.32% of Marty’s laptimes were less than 1.72 minutes.
3. In what proportion of laptimes did it take Marty more than 2 minutes? Interpret your result in the context of the problem.
Use normalcdf ( 2, 999999, 1.84, 0.07 )
About 1.1% of Marty’s laptimes were more than 2 minutes.
4. What laptime is necessary for Marty to be in the fastest 3% of all his laps? Interpret your result in the context of the problem.
Use InvNorm ( .03, 1.84, 0.07 )
Marty will need to have a laptime of 1.71 or less to be in the fastest 3% of all his laps.
More 2.2 Review Problems
5. The EPA fuel economy estimates for automobile models tested recently predicted a Normal model with a mean of
24.8 mpg and a standard deviation of 6.2 mpg.
a. In what interval would you expect the central 68% of autos to be found?
18.6 to 31
b. About what percent of autos should get less than 31 mpg?
84%
c. What percent of cars should get between 31 and 37 mpg?
About 13.41%
d. What percent of cars should get more than 20 mpg?
About 78.06%
e. Describe the gas mileage of the worst 20% of all cars?
x ≤ 19.582
6. Some IQ tests are standardized to a Normal model with a mean of 100 and a standard deviation of 16.
a. What score would begin the interval for the top 16% of all scores? Use the Empirical Rule (68/95/99.7%) to find your answer. Validate this answer using the z-scores table.
x ≥ 116
b. The top 10% of all scores represent the label of “genius”. What is the range of scores for anyone who qualifies as a genius?
x ≥ 120.505
c. What proportion of test takers score a 130 or higher?
About 3.04%
7. While only 5% of babies have learned to walk by the age of 10 months, 75% have earned to walk by 13 months of age. If the age at which babies develop the ability to walk can be described by a Normal Distribution model, find the mean and standard deviation of the Normal model.
Mean = 12.128 months
Std. Dev = 1.294 months
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