Answered

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The population mean annual salary for a environmental compliance specialist is about 63,000A random sample of 30 specialist is drawn from the population.Assume sigma =6,300 What is the probability that the sample mean is less than 60,000

Sagot :

Given:

[tex]\mu=\text{ \$63000 ; n=30 ; }\sigma\text{=6300}[/tex][tex]P(\bar{x}<60000)=P(Z<\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt[]{n}}})[/tex][tex]P(\bar{x}<60000)=P(Z<\frac{60000-63000}{\frac{6300}{\sqrt[]{30}}})[/tex][tex]P(\bar{x}<60000)=P(Z<\frac{-3000}{\frac{6300}{\sqrt[]{30}}})[/tex][tex]P(\bar{x}<60000)=P(Z<-2.608)[/tex][tex]P(\bar{x}<60000)=P(Z<-2.61)[/tex]

From the standard normal table

[tex]P(Z<-2.61)=0.00453[/tex]

Therefore, 0.0045 is the probability of the given sample.

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