We know that

If X is a normally distributed random variable with mean 52 and standard desviation 7, the probability that X is between 45 and 59 is represented as
![P(45Then, we must write 45 and 59 as the mean 52 plus or minus a multiple k of the standard desviation 7[tex]\begin{gathered} 45=\mu+\sigma k \\ 45=52+7k \\ 7k=45-52 \\ k=-1 \end{gathered}]()
So,

By a similar calculation

This means
[tex]P(45taking into account that X is normally distributed and using the 0.68-0.95-0.997 rule[tex]P(\mu-\sigmaSo,
P (45 < X < 59) = 0.68