Answer to Question #193969 in Statistics and Probability for Irish Barrantes

Question

As studied, the average number of hours spent by senior high school students for their online classes a week is 25 hours with a standard deviation of 4 hours. Assuming that the study is true and the data is normally distributed. Find the probability that a randomly selected senior high school srudent spends less than 21 hours or greater than 30 hours.

Answer 1

Let $X=$ the number of hours spent by senior high school students for their online classes a week: $X\sim N(\mu, \sigma^2)$

Then $Z=\dfrac{X-\mu}{\sigma}\sim N(0, 1)$

Given $\mu=25\ h, \sigma=4\ h.$

$$P((X<21)\cup(X>30))$$

$$=P(X<21)+1-P(X\leq30)$$

$$=1+P(Z<\dfrac{21-25}{4})-P(Z\leq\dfrac{30-25}{4})$$

$$=1+P(Z<-1)-P(Z\leq1.25)$$

$$\approx1+0.158655-0.894350\approx0.2643$$

The probability that a randomly selected senior high school srudent spends less than 21 hours or greater than 30 hours is 0.2643.