Question

The manufacturer of a new food additive for beef cattle claims that 80% of the animals fed a diet including this additive should have monthly weight gains in excess of 19 pounds. A large sample of measurements on weight gains for cattle fed this diet exhibits an approximately normal distribution with mean 26 pounds and standard deviation 7 pounds. Do you think the sample information contradicts the manufacturer's claim? (Calculate the probability of a weight gain exceeding 19 pounds.) One standard deviation below the mean is pounds. By the empirical rule, the proportion above this value is approximately %, so the data suggest the manufacturer is probably correct.

Answer 1

using empirical rule , area within one standard dev = 68%

So, area between mean and below one standard dev = 34%

And half of the bell shaped area = 50%

So, area above z=-1 would be =50+34%= 84%