Directions: All questions pertain to normally distributed data. Grab your Z-Score Tables and/or graphing calculator.
1.
In a study of 82 Halo game players, it was found that the ages of these players were normally distributed, with a mean age of 17 years and a standard deviation of 3 years. Were there 15 game players in this study over the age of 21? Justify your answer.
A survey asked a group of high school students about the number of hours of sleep they receive in a 24-hour period. The data was normally distributed with a mean of 7 hours and a standard deviation of 1.25 hours. a) If Harrison slept 8.5 hours, what percent of the students in the survey slept less than Harrison?
b) If your math teacher slept 7.25 hours, what percent of the students in the survey slept more than the teacher? c) What percent of the data in the survey lies in the interval from 5.75 to 8.25? d) What interval about the mean includes 95% of the data in the survey? e) What interval centered about the mean includes 50% of the data in the survey?
3.
The time spent by groups of employees working on new Apple projects has a mean of 18 hours and a standard deviation of 4 hours. a) What is the probability that the amount of time spent by a group is less than 16 hours?
b) What is the probability that the amount of time spent by a group is more than 24 hours?
Professor Aboud has 184 students in his college mathematics lecture class. The scores on the midterm exam are normally distributed with a mean of 72.3 and a standard deviation of 8.9. How many students in the class can be expected to receive a score between 82 and 90? Justify your solution.
A spatial recognition test has a mean score of 92 and a standard deviation of 9.3. Khloe scores 84 and Kim scores 101. What percent of people taking the test would score between Khloe and Kim?
The diameters of evergreen trees in a forested area have a mean of 12 inches and a standard deviation of 3.1 inches. What will be the proportion of trees having a diameter greater than 19 inches?
There are 80 franchises of The Ice Cream Emporium. The gross Saturday ice cream cone sales of the Emporiums show a mean of $5,460 with a standard deviation of $320. What percentage of the Emporiums gross sales of ice cream cones falls between $5,200 and $5,500?
A normal resting llama has a heart rate of 75 beats per minute with a standard deviation of 15 beats per minute. Llamas with a heart rate in the upper 10% of the heart rate distribution may be in need of medical attention. At what heart rate will a llama enter this at-risk group?
Carlos takes a pre-test to be considered as a contestant on a TV trivia game show about mathematics. The people taking the pre-test with Carlos had a mean score of 108 with a standard deviation of 8. Carlos scored 120.
a) What percent of the contestants scored above Carlos? b) Does Carlos' score fall within the middle 50% (IQR) of the scores? c) Contestants are chosen from those scoring above the 75th percentile. What is the cut-off score to be in this group? Will Carlos be in this group of possible contestants?
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