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:
[tex]P(57\lt x\lt65)[/tex]
The z scores is calculated using:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Using the x values it follows:
[tex]z=\frac{57-62}{4}=-1.25[/tex]
Also,
[tex]z=\frac{65-62}{4}=0.75[/tex]
Thus the required probability is:
[tex]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\%[/tex]
Therefore the correct option is C
