Question

The distribution of sample means for monthly employee income at a particular company for samples of 70 employees is​ normal, with a mean of ​$5971 and a standard deviation of ​$219 . You take a random sample of 70 employees from the company and find that their mean monthly income is ​$5 comma 751 . How many standard deviations is the sample mean from the mean of the distribution of sample​ means? Round to one decimal place.

Answer 1

The value is
`z = -8.4`

Explanation:

From the question we are told that

The sample size is n = 70

The mean is
`\mu = \$ 5971`

The standard deviation is
`\sigma = \$ 219`

The sample mean is
`\= x = \$ 5751`

Generally the number of standard deviations the sample mean is from the mean of the distribution is mathematically represented as

`z = (\= x - \mu )/( (\sigma)/(√(n) ) )`

=>
`z = ( 5751 -5971 )/( (219 )/(√( 70 ) ) )`

=>
`z = ( 5751 -5971 )/( (219 )/(√( 70 ) ) )`

=>
`z = -8.4`