1. A test is normally distributed with a mean of 60 and a standard deviation of
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Question
1. A test is normally distributed with a mean of 60 and a standard deviation of 10. Based on the empirical rule, what proportion of the scores are above 80?
2. Based on the empirical rule find the proportion of cases are between minus two standard deviations and minus one standard deviation.
3. On an IQ test with a mean of 100 and a standard deviation of 15, John’s Z score is 1.25. What is John’s score on the IQ test?
4. In a chemistry mid-term exam Mary’s score corresponds to a z score of 2. What percentage of students performed better than Mary? What percentage of students did Mary outperform? Use the empirical rule.
5. The most commonly used IQ test has a mean of 100 and a standard deviation of 15. Based on this test and the empirical rule, what percent of the population qualifies for membership in Mensa (to join you have to have an IQ of 130 or greater)?
6. Find the probability that the number obtained when a die is rolled is an odd number.
7. Which of the following values cannot be a probability? Select all that apply.
a. -0.001
b. 0.5
c. 1.001
d. 0
e. 1
f. 25%
8. A teacher asks 25 of her students to write down their favorite color. The results are presented below:
Color frequency
Red 8
Blue 12
Green 5
If a student is selected at random from the above group of 25, what is the probability that this student likes the red color?
9. The table below shows students distribution per grade in a school.
Grade frequency
1 50
2 30
3 40
4 42
5 38
6 50
If a student is selected at random from this school, what is the probability that this student is in fourth grade?
10. The time taken to fully service a car at XYZ garage is a random variable having a normal distribution of 20 hours and a standard deviation of 2 hours. What is the probability that a car can be fully serviced in this garage in less than 19.5 hours?
Explanation / Answer
1. 2.5% of the scores are above 80
2. the proportion of cases that are between minus two standard deviations and minus one standard deviation is 13.5
7. A,C
8.the probability that this student likes the red color= 8/25=0.32
9. the probability that this student is in fourth grade=42/250=0.168
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