Question

An unknown distribution has a mean of 50 and a standard deviation of ten samples of size n=30 are drawn randomly from population. Find the probability that the sample mean is between 45 and 55.

Answer 1

Solution :

Given that ,

mean = = 50

standard deviation = = 10

n = 30

= = 50

= / n = 10 / 30

P(45 < < 55 )  

= P[(45 - 50) / 10 / 30 < ( - ) / < (55 - 50) / 10 / 30 )]

= P( -2.74 < Z < 2.74 )

= P(Z < 2.74 ) - P(Z < -2.74)

Using z table,  

= 0.9969 - 0.0031

= 0.9938