Question

The standard deviation of a population is 2.50 cms. What is the probability that in a random sample of size 100 the sample mean will differ from the population mean by 0.75 or more?

Select one:  a. 0.9974  b. 0.0013  c. 0.9987  d. 0.0026 

Answer 1

$$\dfrac{|\bar{x}-\mu|}{\sigma/\sqrt{n}}=\dfrac{0.75}{2.5/\sqrt{100}}=3$$

$$P(Z<-3)=0.0013=P(Z>3)$$

$$P(|\bar{x}-\mu|>0.75)=0.0013+0.0013=0.0026$$

d. 0.0026