Question #349659

What is the computed z of the problem stated below? 

The average monthly salary for a call center representative in the Philippines is P 21,700 with a standard deviation of P 6,000. Find the probability that a group of 64 randomly selected call center representatives has an average salary higher than P 22,000 per month.




1
Expert's answer
2022-06-13T16:57:18-0400

Solution:

Let'a denote given values;

μ=21700\mu=21700 P - population mean;

χ=22000\chi=22000 P - sample mean;

σ=6000\sigma=6000 P - standard deviation;

n=64n=64 - sample number.

So, find z score:

z=Xμσn=2200021700600064=0.4;z=\frac{\Chi-\mu}{\frac{\sigma}{\sqrt{n}}}=\frac{22000-21700}{\frac{6000}{\sqrt{64}}}=0.4;

zz score of 0.4 equal 0.6554;0.6554;

We need to find probability of higher than 22000. So 10.6554=0.34461-0.6554=0.3446

P=0.3446=34.46%P=0.3446=34.46\%

Answer:

z=0.4;z=0.4;

P=34.46%.P=34.46\%.


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