Question

1. The distribution of heights of adult men is Normal, with a mean of 69 inches and a standard deviation of 2 inches. Gary’s height has a z-score of 0.5 when compared to all adult men. Interpret what this z-score tells about how Gary’s height.

A. Gary is one standard deviation above the mean.

B. 68% of adult men are shorter than Gary.
C. Gary is 70 inches tall.
D. All of the above are correct answers.

2. The mean length of time, per week, that students at a certain school spend on their homework is Normally distributed with a mean of 14 hours and a standard deviation of 2.4 hours. If Malika is at Q3 in this distribution, this means that Malika spends approximately ___________ hours per week on her homework.

A. 14.0

B. 15.7

C. 16.4

D. 17.5

E. 18.8

1. When you purchase a gallon of pickles, how many pickles should you get? The distribution of the number of dill pickle spears in a gallon container is approximately Normal with a mean of 110 and a standard deviation of 10. When presented with information like this, it is always a good idea to first draw a Normal curve, mark where the mean should be, and note which values are one, two, and three standard deviations away from the mean. Based on your understanding of Normal distributions and the Empirical Rule, which two values should go into the blank boxes below, starting from the box on the left?

   1. 110 and 140

   2. 100 and 120

   3. 90 and 130

   4. 90 and 140

   5. 80 and 110

Answer 1

1) Only C is correct and remaining are false

2) Z-score of 75^th percentile or is Z=0.674

3)

1. 110 and 140 (34+13.5+2.35)%= 49.85%

2. 100 and 120 68%

3. 90 and 130 95%

4. 90 and 140 (95+2.35)%=97.35%

5. 80 and 110    (34+13.5+2.35)%= 49.85%