Question

The Office of Student Services at a large western state university maintains information on the study habits of its full-time students. Their studies indicate that the mean amount of time undergraduate students study per week is 15 hours. The hours studied follows the normal distribution with a standard deviation of 15 hours. Suppose we select a random sample of 100 current students. What is the probability that the mean of this sample is less than 14 hours?

Answer 1

Solution :

Given that,

mean = = 15

standard deviation = = 15

n = 100

= 15

=  / n = 15 / 100=1.5

P( <14 ) = P[( - ) / < (14-15) /1.5 ]

= P(z < -0.67)

Using z table  

=0.2514   

probability=0.2514