Answer to Question #334079 in Statistics and Probability for Esha Flores G Han

Question

2. An electrical company claims that the average life of the bulbs it manufactures is 1 200 hours with a standard deviation of 250 hours. If a random sample of 100 bulbs is chosen, what is the probability that the sample mean will be less than 1150 hours? (5 points)

a. Z = - 2

b. Z = - 3

c. Z = - 4

d. Z = - 5

Answer 1

Let $X=$ the sample mean: $X\sim N(\mu,\sigma^2/n)$

$$P(X<1150)=P(Z<\dfrac{1150-1200}{250/\sqrt{100}})$$

$$=P(Z<-2)\approx0.022750$$