The average salary for a certain profession is $87,500. assume that the standard deviation of such salaries is $26,000. Consider a random sample of 63 people in this profession and let xbar represent the mean salary for the sample. a. What is ? b. What is ?c. Describe the shape of the sampling distributio of ?
d. Find the z-score for the value =80,000.
e. Find P( > 80,000).

Solution :

Given data:

Mean, μ = $87,500

Standard deviation, σ =  $26,000

Sample number, n = 63

a). The value of :

       = 87,500

b). The value of :

        = 3275.69

c). The shape of the sampling distribution is that of a normal distribution (bell curve).

d). The value z-score for the value =80,000.

                = -2.2896

                ≈ -2.29

e). P(x > 80000) = P(z > -2.2896)

                           = 0.9890

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