A cereal manufacturer claims that the gross weight

Question

Problem 19SE

A cereal manufacturer claims that the gross weight (including packaging) of a box of cereal labeled as weighing 12 oz has a mean of 12.2 oz and a standard deviation of 0.1 oz. You gather 75 boxes and weigh them all together. Let S denote the total weight of the 75 boxes of cereal.

a. If the claim is true, what is $P(S \leq 914.8)$?

b. Based on the answer to part (a), if the claim is true, is 914.8 oz an unusually small total weight for a sample of 75 boxes?

c. If the total weight of the boxes were 914.8 oz, would you be convinced that the claim was false? Explain.

d. If the claim is true, what is $P(S \leq 910.3)$?

e. Based on the answer to part (d), if the claim is true, is 910.3 oz an unusually small total weight for a sample of 75 boxes?

f. If the total weight of the boxes were 910.3 oz, would you be convinced that the claim was false? Explain.

Equation transcription:

$P(S\leq{}914.8)$

$P(S\leq{}910.3)$

Text transcription:

P(S \leq 914.8)

P(S \leq 910.3)

Answer 1

Step-by-Step Solution:

Solution

Step 1 of 7

Here we have to find the normal probabilities for the given conditions

The given mean $\mu{}=12.2\ oz$

The given standard deviation is $\sigma{}=0.1\ oz$

Let S denote the weight of the 75 boxes

Then S is a normal variate with mean $\mu{}$ =75(12.2)

=915

Standard deviation=0.1 $\sqrt{75}$

=0.866

Chapter 4, Problem 19SE is Solved

Step 2 of 7

Step 3 of 7

Solution for problem 19SE Chapter 4

A cereal manufacturer claims that the gross weight

Chapter 4, Problem 19SE is Solved