Question

A random sample of size 100 is taken from a population with the mean as 76 and the variance as 256. what is probability of getting sample mean:

a.between 74.4 and 78.4,
b.less than 74.4, and
c.greater than 78.4.

Answer 1

Given the population mean is
`\mu=76` and population standard deviation is
`\sigma=√(256) =16`.

Now sample mean is
`\mu_X=76` and standard deviation of the sample mean is
`\sigma_X=(\sigma)/(√(n)) =(16)/(√(100))=1.6`.

Use Z-score for finding the probabilities. Use a standard normal distribution table.

a)The probability

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b)The probability

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c)The probability

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