Question

The standard deviation of the scores on a skill evaluation test is 320 points with a mean of 1434 points.

If 338 tests are sampled, what is the probability that the mean of the sample would differ from the population mean by less than 43 points? Round your answer to four decimal places.

Answer 1

Given that the scores has mean, say = 1434 and S = 320.

For sample size, n = 338 (large), by Central Limit Theorem,

Hence, The probability that the mean of the sample would differ from the population mean by less than 43 points

=

=

=  ......(Since, and Z is the standard normal variate)

=  

From Standard normal tables,

= 0.99324 0.9932

Hence, the probability that the mean of the sample would differs from the population mean by less than 43 points is 0.9932