Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. statistics
  3. 4. if z is a standard normal random variable, that

4. If Z is a standard normal random variable, that is Z ∼ N(0, 1), (a)...

Free

80.2K

Verified Solution

Question

Statistics

4. If Z is a standard normal random variable, that is Z ∼ N(0,1), (a) what is P(Z 2 < 1)? (b) Find a number c such that P(Z< c) = 0.75 (c) Find a number d such that P(Z > d) = 0.83 (d)Find a number b such that P(−b < Z < b) = 0.95

Answer & Explanation Solved by verified expert
4.1 Ratings (472 Votes)

a) P(Z < 1.000   ) =   0.8413 (answer)

b)Z value at    0.75   =   0.674   (excel formula =NORMSINV(   0.75   ) )

answer: 0.674

c)P(Z > d) = 0.83

P(Z≤d) = 1-0.83 = 0.17

Z value at    0.17   =   -0.954   (excel formula =NORMSINV(   0.17   ) )

answer: -0.954

d)proportion=   0.9500                      
proportion left    0.0500   is equally distributed both left and right side of normal curve                   
z value at   0.025   = ±   1.960   (excel formula =NORMSINV(   0.05   / 2 ) )  

so, value of b = 1.96
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Zin AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Q

(i) How do you understand volatility? (ii) How do we forecast volatility?

Finance
Q

Give example of impulse in sport setting

Medical Sciences
Q

1 As you ride the Ferris wheel your distance from the ground varies with time...

Geometry
Q

Choose the correct description(s) of the pattern below. Then find the the next three numbers.4,...

Basic Math
Q

Use the given data to complete parts a and b below X yo 2 2...

Statistics
Q

3. Determine the cost of the inventory...

Accounting
Q

Which of the following payroll costs are shared equally by the employer and the employee?...

Accounting
Q

Model, Inc., produces model automobiles made from metal. It operates two production departments, Molding and...

Accounting
Q

The general fund is often considered to be the principal financial statement for a governmental...

Accounting
Q

Zeilinger Products, Inc., has a Screen Division that manufactures and sells a number of products,...

Accounting
Q

For how long will Jack have to make payments of $322 at the end of...

Accounting
Q

answer in excel, write clearly, all steps please. Prohlem 2. Citi Rank nfferc vonI...

Finance