Probability of Two University Women being 65.5 Inches or Shorter

Question

The Empirical Rule states that for bell-shaped distributions, about 68% of the values fall within 1 standard deviation of the mean. The heights of women at a large university are approximately bell-shaped, with a mean of 63 inches and standard deviation of 2.5 inches. Use this information to answer the questions. What is the probability that two randomly selected women from this university are both 65.5 inches or shorter? (Give the answer to four decimal places.)

Answer 1

Hello,

I have worked out this problem for you in this video. I hope you find it to be helpful. If you need additional questions, please let me know. Take care!

Dr. Christal-Joy Turner

Answer 2

68% chance of random choice is within 1 standard deviation of the mean Pr(60.5 < x < 65.5)

but Pr(x < 65.5) = 68+32/2 = 68+16 = 84% chance

then calculate odds of two randomly chosen women being less than 65.5 inches.

= (.84)(.84) = .7056 = 70.56%

Your .7079 answer is very close, just off by .0023 = .23% less than 1/2 a percent off