Answer to Question #333257 in Statistics and Probability for Kuro

Question

An electrical company claims that an average life of bulbs it manufacturers is 1200 hours with a standard deviation of 250 hours. If a random sample of 100 bulbs is chosen, what is the probability of the sample mean will be:

a. Greater than 1150 hours?

b. Less than 1250 hours?

c. Betweem 1150 and 1250 hours?

Answer 1

a. $P(X>1150)=1-P(X<1150)=1-P(Z<\frac{1150-1200}{250/\sqrt{100}})=1-P(Z<-2)=1-0.0228=0.9772$

b.$P(X<1250)=P(Z< \frac{1250-1200}{250/ \sqrt{100}})=P(Z<2)=0.9772$

c.P(1150<X<1250)=P(X<1250)-P(X<1150)=0.9772-0.0228=0.9544