Question

In the public schools in Massachusetts, the average number of students per computer for the 2007–2008 school year was 3.1 with a standard deviation of 1.1. A random sample of 42 public schools in the state of Massachusetts was obtained last year.

Determine the mean (in students per computer) of the sampling distribution of the sample mean.

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Calculate the standard deviation (in students per computer) of the sampling distribution of the sample mean. (Round your answer to three decimal places.)

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What is the probability of obtaining a sample average of 2.8 students per computer or more if the average number of students per computer has not changed since the 2007–2008 school year? (Round your answer to four decimal places.)

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Answer 1

a)

= = 3.1

b)

Standard deviation of sampling distribution of sample mean is = / sqrt ( n)

= 1.1 / sqrt ( 42)

= 0.170

c)

P( > x) = P( Z > (x - ) / )

So,

P( >= 2.8) = P(Z > ( 2.8 - 3.1) / 0.170)

= P(Z > -1.76)

= P(Z < 1.76)

= 0.9608 (From Z table)