The average salary for a certain profession is $87,500. assume that the standard deviation of such salaries is $26,000. Consider a random sa

Question

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).

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Adela 5 years 2021-07-19T05:58:45+00:00 1 Answers 70 views 0

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  1. thanhha
    0
    2021-07-19T05:59:48+00:00
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    Solution :

    Given data:

    Mean, μ = $87,500

    Standard deviation, σ =  $26,000

    Sample number, n = 63

    a). The value of $\mu_{x}$ :

       $\mu_x=\mu$

           = 87,500

    b). The value of $\sigma_x$ :

        $\sigma_x = \frac{\sigma}{\sqrt n}$

       $\sigma_x = \frac{26000}{\sqrt {63}}$

            = 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.

       $z-\text{score} =\frac{\overline x - \mu}{\sigma - \sqrt{n}}$

      $z-\text{score} =\frac{80000-87500}{26000 - \sqrt{63}}$

                    = -2.2896

                    ≈ -2.29

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

                               = 0.9890

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