/*! 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. 54 X~N(6,2)Find the probability tha... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Q. 54 (page 387)

X~N(6,2)

Find the probability that xis between three and nine.

Short Answer

Expert verified

The probability that X is between 3 and 9is equal to0.87.

Step by step solution

01

Given Information

Let variable Xhas normal allocation with mean 渭and variance 蟽2.

Then probability density operation is determined by:

f(x)=12蟺蟽e-12(x-渭)2蟽2,x鈭�R

02

Explanation

Let Xhas normal allocation with mean 6 and normal deviation 2,X~N6,22.

Now we require to find the probability that Xis between 3and 9.

We have the following:

P(3<X<9)=鈭�39f(x)dx

Substitute the given expression,

=鈭�3912蟺2e-12(x-6)222dx

=鈭�3612蟺2e-12x-622dx

u=x-62,du=12dx

03

Calculation

Substitute the given expression,

=鈭�-1.51.512蟺e-u22du

=NORMSDIST(1.5)-NORMSDIST(-1.5)

Substract the given expression,

=0.93-0.07

We get,

=0.87.

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

15. Suppose X ~ N(2, 6). What value of x has a z-score of three?

The scores on a college entrance exam have an approximate normal distribution with mean, 碌=52points and a standard deviation, 蟽=11points.

a. About 68%of the y values lie between what two values? These values are ________________. The z-scores are ________________, respectively.

b. About 95%of the yvalues lie between what two values? These values are ________________. The z-scores are ________________, respectively.

c. About 99.7% of the y values lie between what two values? These values are ________________. Thez-scores are ________________, respectively.

The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.3days and a standard deviation of 2.1days.

The 90thpercentile for recovery times is

a. 8.89

b. 7.07

c. 7.99

d. 4.32

The golf scores for a school team were normally distributed with a mean of 68and a standard deviation of three.

Find the probability that a golfer scored between 66and70

Suppose X~N(鈥�3,1). Between what xvalues does 34.14%of the data lie?
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Geometry

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.