SOLUTION: The weight of a miniature Tootsie Roll is normally distributed with a mean of 3.30 grams and standard deviation of 0.13 grams. (a) Within what weight range will the middle 95 pe

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Question 471784: The weight of a miniature Tootsie Roll is normally distributed with a mean of 3.30 grams and standard deviation of 0.13 grams.
(a) Within what weight range will the middle 95 percent of all
miniature Tootsie Rolls fall?
(b) What is the probability that a randomly chosen miniature
Tootsie Roll will weigh more than 3.50 grams?
c) What is the probability that a randomly chosen miniature
Tootsie Roll will weigh between 3.25 and 3.45 grams?

Answer by ewatrrr(24785) About Me  (Show Source):
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Hi,

The weight of a miniature Tootsie Roll is normally distributed with a mean of 3.30 grams and standard deviation of 0.13 grams

(a) Within what weight range will the middle 95 percent of all miniature Tootsie Rolls fall?

Within 2 sd of the mean: sd=.13  range will be: 3.04 to 3.56



P(x>3.50)    

 |z = (3.50-3.30)/.13 = 1.5385

 P(x > 3.50)= 1 -P( z ≤ 1.5385) = 1- .938 = .062



P(between 3.25 abd 3.45)     

|z = (3.25-3.30)/.13 = -.3846  and z = (3.45-3.30)/.13 = 1.1538

P(between 3.25 abd 3.45) = P(z ≤ 1.1538)- P(z ≤ -.3846) = .8757 - .3503 = .5254