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2 years ago

Erik works 55 hours a week making $12.50 hour? His employer pays time and a half for hours over 40. Find his gross pay.

Mathematics

1 answer:

UNO [17]2 years ago

6 0

Answer:

781.25

Step-by-step explanation:

Regular pay = 40*12.50 = 500.00

Overtime = 15*12.5*1.5 = 281.25

Gross pay = 500.00 + 281.25 = 781.25

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For this case we know the following propoertis for the random variable X

$\mu = 83, \sigma = 27$

We select a sample size of n = 81

Part a

Since the sample size is large enough we can use the central limit distribution and the distribution for the sampel mean on this case would be:

$\bar X \sim N (\mu, \frac{\sigma}{\sqrt{n}})$

With:

$\mu_{\bar X}= 83$

$\sigma_{\bar X}=\frac{27}{\sqrt{81}}= 3$

Part b

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$z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And if we find the z score for 89 we got:

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Part c

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We can use the z score formula given by:

$z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

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