Answer:
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.
Step-by-step 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:
[tex]z=\dfrac{X-\mu}{\sigma/\sqrt{n}}=\dfrac{1770-1800}{100/\sqrt{100}}=\dfrac{-30}{10}=-3\\\\\\P(X<1770)=P(z<-3)=0.0013[/tex]
