Question

Homework: Sec. 5.4 Save core: 0 of 1 pt 6 of 8 (5 complete) HW Score: 58.3... 5.4.25 : Question Help The annual salary for one particular occupation is normally distributed, with a mean of about $139,000 and a standard deviation of about $16,000. Random samples of 38 are drawn from this population, and the mean of each sample is determined. Find the mean and standard deviation of the sampling distribution of these sample means. Then, sketch a graph of the sampling distribution. The mean is hy , and the standard deviation is o = U. (Round to the nearest integer as needed. Do not include the $ symbol in your answers.) cents Resour Corr uccess Success edia Libra Enter your answer in the edit fields and then click Check Answer ase Options Pear

Answer 1

1)

Solution :

Given that ,

mean = $\mu$ = 39000

standard deviation = $\sigma$ = 16000

n = 38

$\mu$_{$\bar x$} = $\mu$ = $39000 and

$\sigma$_{$\bar x$} = $\sigma$ / $\sqrt$ n = 16000/ $\sqrt$ 38 = $2595.5427 = $2596

2)

Given that ,

mean = $\mu$ = 62500

standard deviation = $\sigma$ = 5800

n = 43

$\mu$_{$\bar x$} = $\mu$ = 62500 and

$\sigma$_{$\bar x$} = $\sigma$ / $\sqrt$ n = 5800/ $\sqrt$ 43 = 884.4917

P($\bar x$ < 59500) =   P(($\bar x$ - $\mu$ _{$\bar x$} ) / $\sigma$ _{$\bar x$} < (59500 - 62500) / 884.4917)

= P(z < -3.39)   Using standard normal table.   

Probability = 0.0003