A random sample of size n 100 is taken from a population of

A random sample of size n = 100 is taken from a population of size N = 2,500 with mean = 45 and variance 2 = 81.

Solution

A random sample of size n = 100 is taken from a population of size N = 2,500 with mean = 45 and variance 2 = 81.

a-1. Calculate the expected value and the standard deviation of the sample mean. (Negative values should be indicated by a minus sign. Round \"standard deviation\" to 2 decimal places.)

mean =-45

standard error = sd/sqrt(n) =9/sqrt(100) =0.9

a-2. Is it necessary to apply the finite population correction factor Yes or No?

No, 100/2500 =0.04 which is less than 0.05.

b. What is the probability that the sample mean is between 47 and 43? (Round your intermediate calculations to 4 decimal places, \"z\" value to 2 decimal places, and final answer to 4 decimalplaces.)

z value for -47, z=( -47-(-45))/0.9 =-2.22

z value for -43, z=( -43-(-45))/0.9 =2.22

P( -47 <x<-43)= P( -2.22 <z<2.22)

P(z <2.22)- P(z <-2.22)= 0.9868 - 0.0132

= 0.9736

c. What is the probability that the sample mean is greater than 44? (Round your intermediate calculations to 4 decimal places, \"z\" value to 2 decimal places, and final answer to 4 decimal places.)

z value for -44, z=( -44-(-45))/0.9 =1.11

P( X > -44)= P( Z >1.11)

=0.8665