Question

womens heights average 67 inches with a standard deviation of 2.2 inches in a certain study. use the 68 - 95 - 99.7 rule to determine the typical ranges of the womens heights. in what range will approximately the middle 99.7% of the womens heights lie?
the middle 99.7% of the womens heights will lie between □ and □. (simplify your answers. type integers or decimals. use ascending order.)

Explanation:

Step1: Identify mean and standard deviation

Mean $\mu = 67$ inches, standard deviation $\sigma = 2.2$ inches.

Step2: Apply 99.7% rule (3σ range)

Lower bound: $\mu - 3\sigma = 67 - 3\times2.2$
Upper bound: $\mu + 3\sigma = 67 + 3\times2.2$

Step3: Calculate values

Lower bound: $67 - 6.6 = 60.4$
Upper bound: $67 + 6.6 = 73.6$

Answer:

60.4 and 73.6