Answer to Question #264553 in Statistics and Probability for Kenneth

Question

The length, X, in minutes of a MS Teams video lecture for STBE101 is normally distributed

with a mean of 28 minutes and standard deviation of 2 minutes.

(a) Find 𝑃𝑃(20 < 𝑋𝑋 < 28)

(b) Find 𝑃𝑃(𝑋𝑋 > 33)

Answer 1

(a)

$$P(20<X<28)=P(X<28)-P(X\leq 20)$$

$$=P(Z<\dfrac{28-\mu}{\sigma})-P(Z\leq \dfrac{20-\mu}{\sigma})$$

$$=P(Z<\dfrac{28-28}{2})-P(Z\leq \dfrac{20-28}{2})$$

$$=P(Z<0)-P(Z\leq -4)$$

$$=0.5-0.00003167$$

$$=0.49996833$$

(b)

$$P(X>33)=1-P(X\leq 33)$$

$$=1-P(Z\leq \dfrac{33-\mu}{\sigma})$$

$$=1-P(Z\leq \dfrac{33-28}{2})$$

$$=1-P(Z\leq2.5)$$

$$=0.00620967$$