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The U.S. Census Bureau announced that the population mean sales of houses was $322,100. Assume that the standard deviation of the prices is $90,000. If you select a sample size of 100, what’s the cumulative probability that the sample mean will be less than $346,000 for all possible house samples?

Respuesta :

Answer:

P(z < 2.66) = 0.9960

Explanation:

Given that

population mean = 322,100

standard deviation = 90,000

sample mean = 346,000

n = 100

Standard error of mean:

[tex]=\frac{Standard\ Deviation}{\sqrt{n} }[/tex]

[tex]=\frac{90,000}{\sqrt{100} }[/tex]

= 9000

[tex]Z=\frac{Sample\ mean-Population\ mean}{Standard\ error\ of\ mean}[/tex]

[tex]Z=\frac{346,000-322,100}{9,000}[/tex]

z = 2.66

P(z < 2.66) = 0.9960

Above value is computed from the z-tables.

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