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Marianna [84]
3 years ago
11

A shoe manufacturer collected data regarding men's shoe sizes and found that the distribution of sizes exactly fits the normal c

urve. If the mean shoe size is 11 and the standard deviation is 1.5, find:a) What percent of male shoe sizes are greater than 8?
Mathematics
1 answer:
Lina20 [59]3 years ago
7 0

Answer: 97.72%

Step-by-step explanation:

Given : A shoe manufacturer collected data regarding men's shoe sizes and found that the distribution of sizes exactly fits the normal curve.

Let x be the random variable that represents the shoe sizees.

Also, The population mean = \mu=11 ; Standard deviation: \sigma=1.5

Formula for z:-

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

Put x= 8, we get

z=\dfrac{8-11}{1.5}=-2

Now, the probability that the male shoe sizes are greater than 8 :-

P(x>8)=P(z>-2)=1-P(z\leq-2)\\\\=1-0.0227501=0.9772499\approx0.9772

Hence, the percent of male shoe sizes are greater than 8 is 97.72%.

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