Question

Height of 16-year-old girls is normally distributed with a mean of 64 in. and a standard deviation of 2.5 in. Rachel is 5 ft, 5 in. tall.

Select the answer from the drop-down menu to correctly complete the statement.
Based on her raw score of 5 ft, 5 in. Based on her raw score of 5’5 Rachel’s z-score will it be positive or negative?

Answer 1

Answer: To determine whether Rachel's z-score will be positive or negative, we first need to convert her height from feet and inches to inches.

Since there are 12 inches in one foot, Rachel's height in inches can be calculated as:

5 feet x 12 inches/foot + 5 inches = 60 inches + 5 inches = 65 inches

To calculate Rachel's z-score, we can use the formula:

z = (x - μ) / σ

where x is the raw score (in this case, Rachel's height of 65 inches), μ is the population mean (64 inches), and σ is the population standard deviation (2.5 inches).

Substituting the values, we get:

z = (65 - 64) / 2.5

z = 0.4

Since Rachel's height is greater than the mean, her z-score will be positive.

Therefore, the answer is: Positive.

Explanation: