Question

Show all your work. Indicate clearly the methods you use, because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results and explanations. The following histogram shows the relative frequencies of the heights, recorded to the nearest inch, of a population of women. The mean of the population is 64.97 inches, and the standard deviation is 2.66 inches. The figure presents a histogram with 15 bars. The horizontal axis is labeled “Height, in inches,” and the numbers 58 through 72, in increments of 1, are indicated. The vertical axis is labeled “Relative Frequency”, and the numbers 0.00 through 0.20, in increments of 0.05, are indicated. From left to right, the bars begin at a minimum relative frequency, increase to a maximum, and then decrease back to the starting relative frequency, appearing almost symmetric about the center at the height of 65 inches. The data presented by the bars are as follows. 58 inches, 0.01. 59 inches, 0.02. 60 inches, 0.03. 61 inches, 0.04. 62 inches, 0.06. 63 inches, 0.10. 64 inches, 0.15. 65 inches, 0.18. 66 inches, 0.14. 67 inches, 0.11. 68 inches, 0.07. 69 inches, 0.05. 70 inches, 0.02. 71 inches, 0.01. 72 inches, 0.01. One woman from the population will be selected at random. (a) Based on the histogram, what is the probability that the selected woman will have a height of at least 67 inches? Show your work.

Answer 1

0.27

Step-by-step explanation:

To find the probability that the selected woman will have a height of at least 67 inches, we need to find the relative frequency of heights 67 inches or greater and divide it by the total number of heights.

The relative frequency of heights 67 inches or greater is the sum of the relative frequencies for heights 67 inches, 68 inches, 69 inches, 70 inches, 71 inches, and 72 inches. This sum is 0.11 + 0.07 + 0.05 + 0.02 + 0.01 + 0.01 = 0.27.

To find the total number of heights, we need to sum the relative frequencies of all 15 heights. This sum is 0.01 + 0.02 + 0.03 + 0.04 + 0.06 + 0.10 + 0.15 + 0.18 + 0.14 + 0.11 + 0.07 + 0.05 + 0.02 + 0.01 + 0.01 = 1.00.

Therefore, the probability that the selected woman will have a height of at least 67 inches is 0.27 / 1.00 = 0.27.