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The mean per capita income is 23,334 dollars per annum with a standard deviation of 666...

The mean per capita income is 23,334 dollars per annum with a standard deviation of 666 dollars per annum. What is the probability that the sample mean would be less than 23182 dollars if a sample of 168 persons is randomly selected? Round your answer to four decimal places.

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SOLUTION:

From given data,

The mean per capita income is 23,334 dollars per annum with a standard deviation of 666 dollars per annum. What is the probability that the sample mean would be less than 23182 dollars if a sample of 168 persons is randomly selected

The mean per capita income = = 23334

standard deviation = = 666

the sample mean= = 23182

sample = n = 168

The Z score for   = 23182 is

Z = ( - ) / ( / )

= ( 23182 - 23334 ) / (666 / )

=  -152 /  51.383015

Z = - 2.95

The required probability is

P( < 23182 ) = P( z < - 2.95 )

= 0 .00159

0.0016   

Excel function used to find the probability is: = "=NORMSDIST(- 2.95)"

orchestra answered 2 years ago
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