An apple a day.

Question

 An apple a day: A supermarket sells apples in bags labeled as weighing 10 pounds A sample of 50 bags: had a mean weight of 10.3 pounds with standard deviation of 0.1 pound. Someone wants to know the probability that a randomly chosen bag weighs more than 10 pounds. Is enough information given to compute this probability? If s0, compute the probability. If not; explain why not

Answer 1

First of all, the answer is "Yes" , you have all the info you need to find that probability.

Since we have an n=50, we can use the standard normal Z-test to determine this probability. We're given all the information we need to calculate the Z score, which is: (the sample mean-mean)/(standard deviation), which in this case =(10.3-10)/ 0,1. After you do that calculation, look up the number in a table of z-scores, or use your calculator (if it has stat function), to get the p=value. Just make sure you look the right direction! The alternative hypothesis is the p(mean) > 10.0, so you want the prob that the mean is strictly greater than 10. Tables generally tell you or define what prob's they are giving.

Answer 2

compute z = (x - mean)/SD = (10 - 10.3)/0.1 = -3

P(x > 10) = P(z > - 3) = 1 - P(z < -3) = 0.999