Answer to Question #347253 in Statistics and Probability for Air

Question

The amount of time a student taking statistics spends on studying for a test is normally distributed. If the average time spent studying is 10 hours and the standard deviation is 4

hours,

a. What is the probability that a student will spend more than 13 hours studying?

b. What is the probability that a student will spend between 9 to 11 hours studying?

c. What is the probability that a student will spend less than 8 hours studying?

Answer 1

a.

$$P(X>13)=1-P(Z\le\dfrac{13-10}{4})$$

$$=1-P(Z\le0.75)\approx 0.2266$$

b.

$$P(9<X<11)=P(Z<\dfrac{11-10}{4})$$

$$-P(Z\le\dfrac{9-10}{4})$$

$$=P(Z<0.25)-P(Z\le-0.275)\approx 0.1974$$

c.

$$P(X<8)=P(Z<\dfrac{8-10}{4})$$

$$=P(Z<-0.5)\approx0.3085$$