Question

A survey found that​ women's heights are normally distributed with mean 63.5 in. and standard deviation 3.4 in. The survey also found that​ men's heights are normally distributed with mean 69.4 in. and standard deviation 3.8 in. Most of the live characters employed at an amusement park have height requirements of a minimum of 56 in. and a maximum of 64 in. Complete parts​ (a) and​ (b) below. a. Find the percentage of men meeting the height requirement. What does the result suggest about the genders of the people who are employed as characters at the amusement​ park? The percentage of men who meet the height requirement is 7.74 ​%. ​(Round to two decimal places as​ needed.) Since most men do not meet the height​ requirement, it is likely that most of the characters are women. b. If the height requirements are changed to exclude only the tallest​ 50% of men and the shortest​ 5% of​ men, what are the new height​ requirements? The new height requirements are a minimum of 56 in. and a maximum of 64 in.

Answer 1

Refer Standard normal table/Z-table to find the probability or use excel formula "=NORM.S.DIST(-1.4211, TRUE)" & "=NORM.S.DIST(-3.5263, TRUE)" to find the probability.

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Refer Standard normal table/Z-table, Lookup for z-score corresponding to area 0.50 to the left of the normal curve or use excel formula "=NORM.S.INV(0.50)" to find the z-score.

Refer Standard normal table/Z-table, Lookup for z-score corresponding to area 0.05 to the left of the normal curve or use excel formula "=NORM.S.INV(0.05)" to find the z-score.