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Chapter 7: Q. 58 (page 479)

Cereal A company's cereal boxes advertise that each box contains 9.65 ounces of cereal. In fact, the amount of cereal in a randomly selected box follows a Normal distribution with mean 渭=9.70 ounces and standard deviation 蟽=0.03 ounce.

a. What is the probability that a randomly selected box of the cereal contains less than 9.65 ounces of cereal?

b. Now take an SRS of 5 boxes. What is the probability that the mean amount of cereal in these boxes is less than 9.65 ounces?

Short Answer

Expert verified
  1. The resultant probability is 0.0475.
  2. The resultant probability is 0.0001.

Step by step solution

01

Part (a) Step 1: Given information

Given:

The value of Population mean (渭)=9.70

The value of Population standard deviation(s)=0.03

02

Part (a) Step 2: Calculation

Consider the random variable X, which represents the amount of cereal in a box.

The likelihood that a randomly chosen box contains less than 9.65 ounces of cereal can be computed as follows:

P(X<9.65)=Px-渭蟽<9.65-渭蟽=PZ<9.65-9.700.03=P(Z<-1.67)=0.0475

Thus, the required probability is 0.0475.

03

Part (b) Step 1: Given information

The Sample size (n)=5

04

Part (b) Step 2: Calculation

The likelihood that the average amount of cereal in five randomly chosen boxes is less than 9.65ounces can be computed as follows:

P(X炉<9.65)=Px炉-渭蟽n<9.65-渭蟽n=PZ<9.65-9.700.035炉=P(Z<-3.73)=0.0001

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