This Question: 1 pt 3 of 6 (2 complete) This Quiz: 6 pts possible Assume that wo

Question

This Question: 1 pt 3 of 6 (2 complete) This Quiz: 6 pts possible Assume that women's heights are normally distributed with a mean given by =62.5 in, and a standard deviation given by = 2.7 in (a) If 1 woman is randomly selected, find the probability that her height is less than 63 in (b) If 36 women are randomly selected, find the probability that they have a mean height less than 63 in (a) The probability is approximately Round to four decimal places as needed.) (b) The probability is approximately Round to four decimal places as needed.)

Explanation / Answer

= 62.5 = 2.7

(a) X = 63

Z = (X - ) /

= (63 - 62.5) / 2.7

= 0.1852.

The probability from z table is 0.5735.

(b) x = + z/n

63 = 62.5 + z 2.7 / 36

0.5 = z * 2.7 / 6

z = 3 / 2.7

z = 1.1111

From the table, probability is 0.8667.

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