Question

Question 1: Suppose a normal distribution has a mean of 20 and standard deviations away from the mean?

A value of 26 is how many standard deviations away from the mean?
1.5, -1.5, -.05, 0.5

Question 2: A normal distribution has a mean of 20 and a standard deviation of 4. What is the z-score of a value that is 0.52 standard deviations less than the mean? -0.52, -0.13, 0.13, 0.52

Question 3: Suppose the ages of cars driven by employees at the company are normally distributed with a mean of 8 years and a standard deviation of 3.2 years. What is the z-score of a car that is 6 years old? -0.626, 1.6, -1.6, 0.625

Question 4: Suppose a manufacturer makes disposable peppercorn grinders. The number of peppercorns in the grinders is normally distributed with a mean of 322 peppercorns and a standard deviation of 5.3 peppercorns. Suppose the manufacturer will only sell peppercorn grinders with a z-score between -0.9 and 0.9. What are the least and most peppercorns a grinder can contain? least 290; most 354 least 318; most 326 least 308; most 336 least 275; most 369

Question 5: Suppose the velocities of gold swings for amateur golfers are normally distributed with a mean of 96 mph and a standard deviation of 3.9 mph. What is the difference in velocities between a golfer whose z-score is 0 and another golfer whose z-score is -1. 2.9 mph 1.95 mph 3.9 mph 7.8 mph

Answer 1

Answers: See each one below:

1) Sorry, you are missing the standard deviations, so we can't find the z-score.

2) If a score is 0.52 standard deviations from the mean, then the z-score is -0.52. A z-score is by definition the number of standard deviations from the mean.

3) The z-score is -0.625, to find the z-score divide the difference of the value and the mean by the standard deviation. (6 - 8) / 3.2 = -0.625

4) If the z-score is 0.9 or -0.9 we multiply that by the standard deviation and add or subtract that value from the mean. 0.9 x 5.3 = 4.77. Now, subtracting and adding 4.77 to and from the mean gives a range of 317.23 to 326.77.

5) One person is at the mean, with a z-score of 0 and the other is 1 standard deviation below with a z-score of -1. Therefore, he/she is 3.9 mph under.