Please see attached picture Show all work thanks 15. The average starting salary

Question

Please see attached picture Show all work thanks 15. The average starting salary for this year's graduates at a large state university is $46,000 with a standard deviation of $6,000. Furthermore, it is known that the starting salaries are normally distributed. Suppose we selected a sample of 225 students from this year's graduates. The average starting salary of the selected 225 students is the sample mean (o) tt of ple miean 7 (b) [3 PTS] What is the probability that the sample mean is between $45,000 and $46, 500?

Explanation / Answer

a) as sample size is large and population is normally distributed therefore from central limit theorum; distribution of sample mean is normal.

its mean =46000

std error of mean =std deviation/(n)1/2 =6000/(225)1/2 =400

b)

probability that sample mean xbar is betwen 45000 and 46500 =P(45000<X<46500)

=P((45000-46000)/400<Z<(46500-46000)/400)=P(-2.5<Z<1.25)=0.8944-0.0062 =0.8881

please revert for any clarification required

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