Question

The average salary of fresh engineering graduates is $20,000 per year with a standard deviation $2200.

A placement firm conducts a phone survey of 50 randomly selected fresh engineering graduates. Calculate the probability that the aveage salary for this sample is within $800 of the population mean.

What does the question mean by "this sample is within $800 of the population mean"? Answer is 0.990 btw.

Answer 1

the standard deviation is a measure of how far away from the mean you are...

Answer 2

.99 tells us that 99% of the sample is within $800 of $20,000; or rather about 3 standard deviations from it

Answer 3

2.326 sd to be more precise i think

Answer 4

you have to find the standard error which is the standard deviation divided by square root of sample
-> 2200/sqrt(50) = 311.127
this represents the standardized measure of how far the sample mean is from the population mean
since its a normal distribution
800/311.127 = 2.57
probability is the area under normal curve within 2.57 deviations from mean
use a Z table and you will get 0.99

Answer 5

\[z=\frac{x-\mu}{n}\] right?

Answer 6

amistre, its divided by standard error not n

Answer 7

.... youre right :) after awhile the formulas all look alike :)

Answer 8

i was confusing it with a denom of [\(\sigma/\sqrt{n}\)]

Answer 9

exactly :)

Answer 10

Ah you guys are saviours, I had already screenshot your explanation :) thanks so much!