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.
1 answer:
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:

The z scores is calculated using:

Using the x values it follows:

Also,

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\%](https://tex.z-dn.net/?f=P%28-1.25The%20proability%20is%3A%5Btex%5DP%28-1.25This%20can%20be%20expressed%20as%20percentage%20as%3A%5Btex%5DP%28-1.25%5Clt%20z%5Clt0.75%29%3D66.8%5C%25)
Therefore the correct option is C
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