You are on the right track by finding the z-score of 67 inches. However, we want to find the probability that the tallest of the three women is taller than 67 inches.
The probability that a single woman is taller than 67 inches is 0.1977, which you have correctly found. We now need to find the probability that all three women are shorter than 67 inches. The probability that a single woman is shorter than 67 inches is 1 - 0.1977 = 0.8023. Since their heights are independent, the probability that all three women are shorter than 67 inches is 0.8023^3 = 0.5164.
Finally, the probability that at least one of the three women is taller than 67 inches (which is the same as the tallest of the three women being taller than 67 inches) is 1 - 0.5164 = 0.4836. This is your final answer.
The heights of women in a certain population have a Normal distribution with mean 64 inches and standard deviation 3.5 inches. We select three women at random from this population. Assume that their heights are independent. Find the probability that the tallest of these three women will be taller than 67 inches.
My work:
(67-64)/3.5 = 0.857, using the z-score table I then get 0.8023, I then subtracted this from 1 to get 0.1977. But, it's not the right answer.
Appreciate any help I can get!
1 answer
1 answer