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maria [59]
1 year ago
13

Suppose a normal distribution has a mean of 62 and a standard deviation of4. What is the probability that a data value is betwee

n 57 and 65? Round youranswer to the nearest tenth of a percent.

Mathematics
1 answer:
saw5 [17]1 year ago
8 0

SOLUTION

From the given data the mean is 62 and standard deviation is 4

It is required to find the probability that a data value is between 57 and 62

That is:

P(57\lt x\lt65)

The z scores is calculated using:

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

Using the x values it follows:

z=\frac{57-62}{4}=-1.25

Also,

z=\frac{65-62}{4}=0.75

Thus the required probability is:

P(-1.25The proability is:[tex]P(-1.25This can be expressed as percentage as:[tex]P(-1.25\lt z\lt0.75)=66.8\%

Therefore the correct option is C

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