Answer to Question #257743 in Statistics and Probability for Manu

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

$z=\frac{\overline{x}-\mu}{\sigma/\sqrt n}=\frac{0.75}{2.5/10}=3.00$

$P(z>3.00)=1-P(z<3.00)=1-0.9987=0.0013$

Answer: b. 0.0013