I'm trying to understand how to do this problem. We are using minitab and I think I have the correct answer but it would be helpful for someone to explain it to me.
The question is:
The daily sales of a certain variety store are approximately normally distributed with a mean of 1000, and a standard deviation of 200. What is the approximate probability that a random sample of 100 days will yield a mean between 980 and 1040?
a) .1191 b) .9500 c) .8185 d) 9030
The answer I got with Minitab from doing:
Graph > Probability Distribution Plot > View Probability >
(Distribution = normal, Mean = 1000, Standard deviation = 200) > Shaded Area (X Value, Middle, X1 = 980, x2 = 1040).
.1191 is the answer I got but I don't understand where the 100 days comes in.
Could someone please explain this to me?
Best Answer
We are looking at the average of 100 days' worth of sales. You're being asked to calculate the probability that this average is between 980 and 1040, not the prob that one day's sales are between 980 and 1040.
The average of 100 days of sales has approximately normal distribution with mean 1000, but the standard deviation of that average is $200/\sqrt{100}=20$.