A survey found that women\'s heights are normally distrubted with mean in 63.8 i

Question

A survey found that women's heights are normally distrubted with mean in 63.8 in and standard deviation 3.7 in. The survey also found that men's heights are normally distribued with mean 68.6 in and standard deviation 3.3 in. Most of the live characters employed at an amusement park have height requirements of a minumum of 57 in and a maximum of 64 in. Complete parts (a) and (b) below.

A) Find the percentage of men meeting the height requirment. 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 requirment is ___%

B) If the height requirments are changed to exlude only the tallest of 50% of men and the shortest 5% of men, what are the new height requirments?

The new height requirments are a mimimum of ___ in and a maximum of ____in

Explanation / Answer

a) P(57<X<54)

= P((57-68.6)/3.3<Z<(64-68.6)/3.3)

= P(-3.52<Z<-1.39)

= 8.14%

b) Tallest 50% = 0*3.3+68.6 = 68.6

Shortest 5% =- -1.645*3.3+68.6 = 63.17

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