Give an estimate use 997 rule aka empirical rule

95% of the math scores lie between what two values? (Give an
estimate )
Use the 68-95-99.7 Rule (aka Empirical Rule). About 95% of the scores lie within 2
standard deviations of the mean. That means 95% of the math scores lie between
70-2(10) and 70+2(10) = 50 and 90.
i. Bob scores 85 on each exam. On which exam did he perform better,
compared to his classmates?
Compare Z scores on the two exams. From part b, Bob’s Z score on the math exam
is 1.5. On the stat exam, Bob’s Z score is = 1.0. Bob did better
on the math exam.
1

2. Data are collected on the fuel economy of 2001 model midsize cars. The information
measured in average miles per gallon (MPG) is summarized below.
MPG
Frequency
32 30 28 26 24 22
7
6
5
4
3
2
1
0
Histogram of MPG
Descriptive Statistics: MPG
Total
Variable Count Mean StDev Minimum Q1 Median Q3 Maximum
MPG 32 26.750 2.874 22.000 24.000 26.500 28.750 33.000
Can the 68-95-99.7 rule be applied to this data to give an approximate range
where 95% of the MPG lie? Explain why or why not.
No; data are not close to a normal distribution
3. Bob’s Z-score on a psychology exam is 0.25. What is the correct interpretation?
a. Bob’s score is at the 25 th percentile.
b. Bob got a 25 on the exam.
c. Bob’s score is 25 percentage points above the mean.
d. Bob’s score is 0.25 standard deviations above the mean.