Question

A new lightbulb has been developed with a mean lifetime of 1800 hours and standard deviation of 100 hours. A sample of 100 of these bulbs is tested. The sample mean lifetime is 1770 hours. (a) What is the probability of obtaining a sample mean that is less than or equal to 1770 hours? (5 points) (b) Would it be unusual to obtain a sample mean of less than or equal to 1770 hours? (5 pts

Answer 1

a) The probability of obtaining a sample mean that is less than or equal to 1770 hours is P(M≤1770)=0.0013.

b) It is unusual, as there are only 13 chances in 10,000 (0.13%) of having this outcome.

Explanation:

We have a population lifetime with mean of 1800 hours and standard deviation of 100 hours.

Samples of size n=100 are taken and tested.

We can calculate the probability of obtaining a sample mean that is less than or equal to 1770 hours using a z-score for the sample Mean M=1770 and then calculating its probability according to the standard normal distribution:

`z=(X-\mu)/(\sigma/√(n))=(1770-1800)/(100/√(100))=(-30)/(10)=-3\\\\\\P(X<1770)=P(z<-3)=0.0013`