Suppose a simple random sample of size nequals81 is obtained from a population with mu equals 79 and sigma equals 18. (a) Describe the sampling distribution of x overbar. (b) What is Upper P (x overbar greater than 81.2 )? (c) What is Upper P (x overbar less than or equals 74.4 )? (d) What is Upper P (77.6 less than x overbar less than 83.2 )?

(a) The sampling distribution of = Population mean = 79

(b)  P ( greater than 81.2 ) =  0.1357

(c) P ( less than or equals 74.4 ) = .0107

(d) P (77.6 less than less than 83.2 ) = .7401

Step-by-step explanation:

Given -

Sample size ( n ) = 81

Population mean = 79

Standard deviation = 18

(a) Describe the sampling distribution of

For large sample using central limit theorem

the sampling distribution of = Population mean = 79

(b) What is Upper P ( greater than 81.2 ) =

 =

                    =  

                    =

                    = 1 - .8643 =

                    = 0.1357

(c) What is Upper P ( less than or equals 74.4 ) =

=

                    =

                    = .0107

(d) What is Upper P (77.6 less than less than 83.2 ) =

=

                                =

                                 =

                                  = 0.9821 - .2420

                                   = 0.7401

it is 10.6 according to my calculations