Question

There are 60 calories on average in a Tootsie Roll Pop with a standard deviation of 2 calories. Assume that the calories are normally distributed. What is the probability that a randomly selected Tootsie Roll Pop has less than 55 calories? (round to four decimals) What is the probability that the mean number of calories of a sample of 12 Tootsie Roll Pops have less than 55 calories? (round to four decimals)

Answer 1

Let X denote the calories in a Tootsie Roll Pop

X~N(60,4)

(a) P[X<55]=

- 60 -) = (-5/2) = 0.0062

(b)

X follows N(60,4/12) = N(60,1/3)

Hence
55 - 60 PLX < 55) = 147,0) = 2.353 * 10-1

So if rounded upto 4 decimals then the answer should be 0.