Find the area under the standard normal probability distribution between the following pairs of z-scores:

a)z=0andz=2.00

b)z=0andz=3

c)z=0andz=1.5

d)z=0andz=.80


Short Answer

Expert verified

A probability distribution is a statistical distribution that specifies all potential values as well as potential outcomes for a random variable within a particular range. The likelihood of an event happening. A probability distribution is a table as well as a formula that associates every result of a statistical study with its occurrence probability.

Step by step solution

01

(a) The data is given below

The calculation is given below:

z=0andz=2

To find the area between 0 and 2 are:


P(0<z<2)=0.4772

The chart is given below:

02

(b) The data is given below

The calculation is given below:


z=0andz=3

To find the area between 0 and 3 are:

P(0<z<3)=0.4987

The chart is given below:

03

(c) The data is given below

The calculation is given below:


z=0andz=1.5

To find the area between 0 and 1.5 are:

P(0<z<1.5)=0.4332

The chart is given below:

04

(d) The data is given below

The calculation is given below:

z=0andz=0.80

To find the area between 0 and 0.80 are:

P(0<z<0.80)=0.2881

The chart is given below:

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 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

Assume that xhas an exponential distribution withθ=3.

Find

a.P(x1)

b.P(x>1)

c.P(x=1)

d.P(x6)

e.P(2x10)

The Apprenticecontestants’ performance ratings. Referto the Significance(April 2015) study of contestants’ performanceson the United Kingdom’s version of the TVshow, The Apprentice, Exercise 2.9 (p. 73). Recall thatthe performance of each of 159 contestants was rated ona 20-point scale. Contestants were also divided into twogroups: those who played for a job and those who playedfor a businesspartnership. These data (simulated, based onstatistics reportedin the article) are saved in the accompanyingfile. Descriptive statistics for each of the two groupsof contestants are displayed in the accompanying Minitabprintout.

a. Determine whether the performance ratings of contestantswho played for a job are approximately normallydistributed.

b. Determine whether the performance ratings of contestantswho played for a business partnership are approximatelynormally distributed.

Descriptive Statistics: Rating

Variable Rating

Price

N

Mean

St.Dev

Minimum

Q

1

median

Q3

Maximum

IQ

R

Job

99

7.879

4.224

1

4

9

11

20

7

Partner

60

8.883

4.809

1

5

8

12

20

7

If x is a binomial random variable, use Table I in Appendix D to find the following probabilities:

a.for n = 10, p = .4

b.for n = 15, p = .6

c.for n = 5, p = .1

d.for n = 25, p = .7

e.for n = 15, p = .9

f.for n = 20, p = .2

Find each of the following probabilities for the standard normal random variable z:

a.P(-z1)b.P(-1.96z1.96)c.P(-1645z1.645)d.P(-2z2)

If x is a binomial random variable, calculate , , and for each of the following:

  1. n = 25, p = .5
  2. n = 80, p = .2
  3. n = 100, p = .6
  4. n = 70, p = .9
  5. n = 60, p = .8
  6. n = 1000, p = .04
See all solutions

Recommended explanations on Math Textbooks

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