Hi, I was doing this problem and I am confused because I\'m not sure whether my

Question

Hi, I was doing this problem and I am confused because I'm not sure whether my teacher did it correctly. To my understanding we find the reduced standard deviation which is .2, the mean that was previously stated is 12. So 11.6 is 3 standard deviations below the mean in respect to .2, correct? My teacher stated that it is 2 below the mean. I was hoping you could clarify his reasoning.

If a random sample of 4 bags of jelly beans is selected what is the probability that the sample average will be greater than 11.6? (Use empirical rule.)

A) 84% B) 95% C) 99.7% D) 97.5% E) 16%

His analysis....

If the underlying population is normal, then the distribution of x-bar is also normal with the same mean (12) but with reduced standard deviation (.4/sqrt(4) = .2). So the area to the right of 11.6 is 1 minus the area to the left of 11.6 and 11.6 is 2 standard deviations bellow the mean. Therefore, the answer is 1 – 2.5% = 97.5%.

Explanation / Answer

as we know that z score =(X-mean)/std deviaion

now as you have notified that std deviation =0.2

theefore z score for 11.6 =(11.6-12)/0.2 =-2

hence he is right that 11.6 is 2 std deviation below from mean, for whcih 97.5% is correct

please reply if above is clear.

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