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Chapter 7: Q. 57 (page 479)

Bottling cola A bottling company uses a filling machine to fill plastic bottles with cola. The bottles are supposed to contain 300 milliliters (ml). In fact, the contents vary according to a Normal distribution with mean 渭=298mland standard deviation 蟽=3ml.

a. What is the probability that a randomly selected bottle contains less than 295ml?

b. What is the probability that the mean contents of six randomly selected bottles is less than 295ml?

Short Answer

Expert verified

(a). the probability that a randomly selected bottle contains less than 295mlis 15.87%

(b). the probability that the mean contents of six randomly selected bottles is less than is0.71%

Step by step solution

01

Part(a) Step 1: Given information 

Given,

渭=298蟽=3x=295

Use the following formulae

z=x-渭蟽

02

Part(a) Step 2: Calculation

The z-score is

z=x-渭蟽=295-2983=-1.00

The likelihood of associating using the normal probability P(Z<-1.00)is given in the row starting with -1.0and in the column starting with .00of the standard normal probability

P(x<295)=P(Z<-1.00)=0.1587=15.87%

03

Part(b) step 1: Given information 

Given,

渭=298蟽=3n=6x=295
04

Part(b) Step 2: Calculation

Because the population distribution is normal, so is the sampling distribution of the sample mean x炉.

The z-score is

z=x-渭x炉炉蟽x炉炉=x炉-渭dn=295-2983n炉=-2.45

The associating probability using the normal probability P(Z<-2.45)is given in the row starting with -2.4and in the column starting with .05of the standard normal probability

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Most popular questions from this chapter

Airline passengers get heavier In response to the increasing weight of airline passengers, the Federal Aviation Administration (FAA) told airlines to assume that passengers average 190 pounds in the summer, including clothes and carry-on baggage. But passengers vary, and the FAA did not specify a standard deviation. A reasonable standard deviation is 35 pounds. A commuter plane carries 30 passengers. Find the probability that the total weight of 30 randomly selected passengers exceeds 6000 pounds.

Which one of the following would be a correct interpretation if you have a z-score of +2.0 on an exam?

a. It means that you missed two questions on the exam.

b. It means that you got twice as many questions correct as the average student.

c. It means that your grade was 2 points higher than the mean grade on this exam.

d. It means that your grade was in the upper 2% of all grades on this exam.

e. It means that your grade is 2 standard deviations above the mean for this exam.

Songs on an iPod Refer to Exercise 53 . How many songs would you need to sample if you wanted the standard deviation of the sampling distribution ofx-x炉 to be 10 seconds? Justify your answer.

What does the CLT say? Asked what the central limit theorem says, a student replies, "As you take larger and larger samples from a population, the histogram of the sample values looks more and more Normal." Is the student right? Explain your answer.

At a particular college, 78%of all students are receiving some kind of financial aid. The school newspaper selects a random sample of 100students and 72%of the respondents say they are receiving some sort of financial aid. Which of the following is true?

  1. 78%is a population and 72%is a sample.
  2. 72%is a population and 78%is a sample.
  3. 78%is a parameter and 72%is a statistic.
  4. 72%is a parameter and 78%is a statistic.
  5. 72%is a parameter and 100is a statistic.
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