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Natalija [7]
3 years ago
8

A survey found that​ women's heights are normally distributed with mean 63.2 in. and standard deviation 2.4 in. The survey also

found that​ men's heights are normally distributed with a mean 67.2 in. and standard deviation 2.7. Complete parts a through c below. a. Most of the live characters at an amusement park have height requirements with a minimum of 4 ft 9 in. and a maximum of 6 ft 2 in. Find the percentage of women meeting the height requirement?
Mathematics
1 answer:
Effectus [21]3 years ago
8 0

Answer: 99.51%

Step-by-step explanation:

Given : A survey found that​ women's heights are normally distributed.

Population mean : \mu =63.2  \text{ inches}

Standard deviation: \sigma= 2.4\text{ inches}

Minimum height = 4ft. 9 in.=4\times12+9\text{ in.}=57\text{ in.}

Maximum height = 6ft. 2 in.=6\times12+2\text{ in.}=74\text{ in.}

Let x be the random variable that represent the women's height.

z-score : z=\dfrac{x-\mu}{\sigma}

For x=57, we have

z=\dfrac{57-63.2}{2.4}\approx-2.58

For x=74, we have

z=\dfrac{74-63.2}{2.4}\approx4.5

Now, by using the standard normal distribution table, we have

The probability of women meeting the height requirement :-

P(-2.58

Hence, the percentage of women meeting the height requirement = 99.51%

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