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krek1111 [17]
3 years ago
14

A survey found that women's heights are normally distributed with mean 62.6 in. And standard deviation 2.5 in. The survey also f

ound that men's heights are normally distributed with mean 68.3 in. And standard deviation 3.3 in. Most of the live characters employed at an amusement park have height requirements of a minimum of 57 in. And a maximum of 64 in. 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?
Mathematics
1 answer:
Soloha48 [4]3 years ago
7 0

Answer:

The new height requirements are minimum of 64.1875 inches and maximum of 68.3 inches

Step-by-step explanation:

To exclude the tallest 50% of men and shortest 5% of men, we need to find the critical z-value for a significance level of 0.5 & 0.05 and then solve for x in the z-score equation.

For significance value of 0.5, z = 0

We are given;

μ = 68.3 in

σ = 2.5 in

Thus from z = (x - μ)/σ, we have;

0 =(x - 68. 3)/2.5

0 = x - 68. 3

x = 68.3 inches for men max

Similarly, for significance value of 0.05, z = -1.645

Thus to find x;

-1.645 = (x - 68. 3)/2.5

-4.1125 = x - 68.3

x = 68.3 - 4.1125

x = 64.1875 inches for men min

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