Question

in a certain study, womens heights are found to be approximately normally distributed with a mean of 62 inches and a standard deviation of 2.5 inches.
a. what would be the z - score for a woman who is 5 feet 8 inches tall?
b. what percentage of women is she taller than?
click the icon to view a table of z - scores and percentiles.
a. the z - score for the womans height is 2.4. (round to one decimal place as needed.)
b. she is taller than % of women. (round to two decimal places as needed.)

Explanation:

Step1: Recall z - score and percentile relationship

The z - score is used to find the percentile in a standard normal distribution table.

Step2: Look up the percentile for z = 2.4

Looking up z = 2.4 in the standard normal distribution table (z - score and percentiles table), the area to the left of z = 2.4 represents the percentage of values less than the value corresponding to z = 2.4. The area to the left of z = 2.4 is approximately 0.9918.

Step3: Calculate the percentage of women shorter

The percentage of women shorter than the woman with z - score 2.4 is 99.18%.

Step4: Calculate the percentage of women taller

The percentage of women she is taller than is \(100 - 99.18=0.82\)%.

Answer:

b. 99.18%