A normal population has a mean of 55 and a standard deviation of 14. You select a random sample of 25. Compute the probability that the sample mean is: (Round your z values to 2 decimal places and final answers to 4 decimal places): Greater than 59. Less than 54. Between 54 and 59.

(1) The probability that the sample mean  is  Greater than 59 = 0.778

(2) The probability that the sample mean  is  less than 59 = .3632

(3) The probability that the sample mean  is  is Between 54 and 59 = 0.559

Step-by-step explanation:

Given -

Mean = 55

Standard deviation = 14

Sample size ( n ) = 25

the probability that the sample mean  is  Greater than 59 =

  =  

                 =  

                  = 1 -

                  =  1 - 0.9222 = .0778

the probability that the sample mean is  Less than 54 =

  =

                    =

                    =  .3632

the probability that the sample mean is Between 54 and 59 =

=

                         =

                          =

                          = .9222 - .3632

                           = 0.559

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step-by-step explanation: