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

A random sample of size n = loo is taken from a population of size N = 2,500 with mean p = -45 and variance sigma^2 = 81. Use Table 1. a-1. Is it necessary to apply the finite population correction factor? Yes No a-2. Calculate the expected value and the standard error of the sample mean. (Negative values should be indicated by a minus sign. Round standard error to 2 decimal places.) Expected value Standard error b. What is the probability that the sample mean is between -47 and -43? (Round intermediate calculations to 4 decimal places, z value to 2 decimal places, and final answer to 4 decimal places.) Probability c. What is the probability that the sample mean is greater than -44? (Round intermediate calculations to 4 decimal places, z value to 2 decimal places, and final answer to 4 decimal places.) Probability

Solution

(a-1) No

--------------------------------------------------------------------------------------------------------------------

(a-2)

expected value=-45

standard error= s/vn= sqrt(81/100) =0.9

--------------------------------------------------------------------------------------------------------------------

(b)P(-47<xbar<-43) = P((-47+45)/0.9 <(xbar-mean)/(s/vn)<(-43+45)/0.9)

=P(-2.22<Z<2.22) =0.9736 (from standard normal table)

--------------------------------------------------------------------------------------------------------------------

(c)P(xbar>-44) = P(Z>(-44+45)/0.9)

=P(Z>1.11) = 0.1335 (from standard normal table)