In the advertisements for a large university, the dean of the School of Business
ID: 3356522 • Letter: I
Question
In the advertisements for a large university, the dean of the School of Business claims that the average salary of the school's graduates one year after graduation is normally distributed within a mean of $800 per week with a standard deviation of $100.
A. What is the probability that the sample of 25 people who graduate one year ago will have a mean salary below $750 per week?
B. Find a symmetrically distributed interval around that will include 95% of the sample means when the sample size is 25.
Explanation / Answer
= 800 = 100
A. x' = 750
z = (x' - ) /
= (750 - 800) / 100
= -50 / 100
= -0.5
From the z table, the probability is 0.3085
B. Let the interval be (a,b).
a = - z / n
= 800 - 1.96*100 / 25
= 800 - 196/5
= 800 - 39.2
= 760.8.
b = + z / n
= 800 + 1.96*100 / 25
= 800 + 196/5
= 800 + 39.2
= 839.2.
The interval is (760.8, 839.2).
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