SOLUTION: Hello, I do not wish for you to work the problem unless I did it wrong. I'm simply looking to make sure that I am grasping the information correctly. So, Here is my statics q

Question 884408: Hello, I do not wish for you to work the problem unless I did it wrong. I'm simply looking to make sure that I am grasping the information correctly.
So, Here is my statics question: The average cost of XYZ brand running shoes is $83 per pair with a standard deviation of $8 (σ = 8). If nine pairs of running shoes are selected (n = 9), find the probability that the mean cost of a pair of shoes will be less than $80: Assume that the variable is normally distributed.
I've worked the problem and I THINK the answer is .8686 However, I am unsure of myself. Could you tell me if I am right? This is how I worked it:
80-83/ 8/√9= 3/2.66= 1.125
Looking at the Cumulative Standard Normal Distribution chart, I would go to the 1.1 in the z column and then move to the right to the .02 row. if so, then my answer is .8686
did I miss any steps? I really appreciate your help.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
Your calculated z-value should be -1.125 and round it to -1.13, then
Pr(X<80) = 0.1292
Note that the sample size is really small, usually a sample size this small drives us to use the t-distribution BUT the problem states we should use the normal distribution.
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