Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 2: Q 87. (page 143)

The weights of laboratory cockroaches can be modeled with a Normal distribution having mean 80 grams and standard deviation 2 grams. The following figure is the Normal curve for this distribution of weights.

Point C on this Normal curve corresponds to

a.84grams.b.82grams.c.78grams.d.76grams.e.74grams.

Short Answer

Expert verified

The correct option is (b) 82grams

Step by step solution

01

Given information

Population mean (μ)=80

Population standard deviation (s)=2

02

Calculation

Consider X to be a random variable that represents cockroach weight in grams.

The percentage of cockroaches weighing between 76 and 84 grams is computed as follows:

P(76<X<84)=P(76−μσ<Z<84−μσ)=P(76-802<Z<84-802)=P(−2<Z<2)=0.95

Thus, the required proportion is approximately 95%

Hence, the correct option is(b)

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Put a lid on it! Refer to Exercise 56. The supplier is considering two changes to reduce the percent of its large-cup lids that are too small to less than 1%. One strategy is to adjust the mean diameter of its lids. Another option is to alter the production process, thereby decreasing the standard deviation of the lid diameters.

(a) If the standard deviation remains at σ=0.02inches, at what value should the supplier set the mean diameter of its large-cup lids to ensure that less than 1%are too small to fit? Show your method.

(b) If the mean diameter stays at μ=3.98inches, what value of the standard deviation will result in less than 1%of lids that are too small to fit? Show your method.

(c) Which of the two options in (a) and (b) do you think is preferable? Justify your answer. (Be sure to consider the effect of these changes on the percent of lids that are too large to fit.)

Standard Normal areas Find the proportion of observations in a standard Normal distribution that satisfies each of the following statements.

a. z<−2.46

b. 0.89<z<2.46

Refrigerators Refer to Exercise 75

a. Use your calculator to make a Normal probability plot of the data. Sketch this graph on your paper.

b. What does the graph in part (a) imply about whether the distribution of refrigerator capacity is approximately Normal? Explain.

Quiz scores The scores on Ms. Martin’s statistics quiz had a mean of 12 and a standard deviation of 3Ms. Martin wants to transform the scores to have a mean of 75 and a standard deviation of 12What transformations should she apply to each test score? Explain your answer.

Run fast Peter is a star runner on the track team. In the league championship meet, Peter records a time that would fall at the 80th percentile of all his race times that season. But his performance places him at the 50th percentile in the league championship meet. Explain how this is possible. (Remember that shorter times are better in this case!)
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free