/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q 88. The weights of laboratory cockro... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Q 88. (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.

About what proportion of the cockroaches will have weights greater than 83 grams?

a.0.0228b.0.0668c.0.1587d.0.9332e.0.0772

Short Answer

Expert verified

The correct option is (b)0.0668

Step by step solution

01

Given information

Population mean (渭)=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 more than 83 grams is computed as follows:

P(X>83)=P(x鈭�渭蟽>83鈭�渭蟽)=P(Z>83鈭�802)=P(Z>1.5)=0.0668

Thus, the required proportion is approximately 0.0668

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

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

Class is over! Mr. Shrager does not always let his statistics class out on time. In fact, he seems to end class according to his own 鈥渋nternal clock.鈥� The density curve models the distribution of the amount of time after class ends (in minutes) when Mr. Shrager dismisses the class. (A negative value indicates he ended class early.)

a. What height must the density curve have? Justify your answer.

b. About what proportion of the time does Mr. Shrager dismiss class within 1 minute of its scheduled end time?

c. Calculate and interpret the 20thpercentile of the distribution.

Step right up! Refer to Exercise 22 Suppose that the distances from the tops of the students鈥� heads to the ground are converted from inches to feet (note that 12in.=1ft).

a. What shape would the resulting distribution have? Explain your answer.

b. Find the mean of the distribution of distance in feet.

c. Find the standard deviation of the distribution of distance in feet.

I think I can! Refer to Exercise 55. The locomotive鈥檚 manufacturer is considering two changes that could reduce the percent of times that the train arrives late. One option is to increase the mean adhesion of the locomotive. The other possibility is to decrease the variability in adhesion from trip to trip, that is, to reduce the standard deviation.

(a) If the standard deviation remains at 蟽=0.04, to what value must the manufacturer change the mean adhesion of the locomotive to reduce its proportion of late arrivals to less than 2%of days? Show your work.

(b) If the mean adhesion stays at渭=0.37, how much must the standard deviation be decreased to ensure that the train will arrive late less than 2%of the time? Show your worK

(c) Which of the two options (a) and (b) do you think is preferable?. justify your answer. (Be sure to consider the effect of these changes on the percent of days that the train arrives early to the switch point)

Measure up Clarence measures the diameter of each tennis ball in a bag with a standard ruler. Unfortunately, he uses the ruler incorrectly so that each of his measurements is 0.2inchtoo large. Clarence鈥檚 data had a mean of 3.2inchesand a standard deviation of 0.1inch (Recall that 1in.=2.54cm)

a. Find the mean of the corrected measurements in centimeters.

b. Calculate the standard deviation of the corrected measurements in centimeters.

Post office A local post office weighs outgoing mail and finds that the weights of first-class letters are approximately Normally distributed with a mean of 0.69 ounces and a standard deviation of 0.16 ounces.

a. Estimate the 60th percentile of first-class letter weights.

b. First-class letters weighing more than 1 ounce require extra postage. What proportion of first-class letters at this post office requires extra postage?
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

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.