Question

An unknown distribution has mean 82 and a standard deviation of 11.2. Samples of size n = 35 are drawn randomly from the population. Find the probability that the mean of the sample means is between 81.2 and 83.6.

Answer 1

Solution :

Given that ,

mean = = 82

standard deviation = = 11.2

n = 35

=

=  / n= 11.2 / 35=1.89

P(81.2<     <83.6 ) = P[(81.2 - 82) /1.89 < ( - ) /   < (83.6-82) / 1.89)]

= P(-0.42 < Z <0.85 )

= P(Z <0.85 ) - P(Z < -0.42)

Using z table

=0.8023-0.3372

=0.4641

probability= 0.4651

probability=