Question

In a survey conducted by the National Center for Health Statistics, the sample mean height of women in the United States ages 20-29 was 64.2 inches, with a standard deviation of 2.9 inches. Suppose the data is symmetric. Estimate the percent of women whose heights are between 64.2 and 67.1 inches. (Chebyshev's Thereom and/or Empirical Rule)

Answer 1

Solution :

Given that,

Using Empirical rule,

P( - 1< X < + 1) = 68%

P( - 2< X < + 2) = 95%

P( - 3< X < + 3) = 99.7%

P(64.2 < X < 67.1) = P(X < 67.1) - P(X < 64.2) = 0.84 - 0.50 = 0.34 = 34%