1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
nataly862011 [7]
3 years ago
5

Define z_alpha to be a z-score with an area of alpha to the right. For Example: z_0.10 means P(Z > z_0.10) = 0.10. We would a

lso have, for example; P(Z < -z_0.10) = 0.10 because of the symmetric property of the normal distribution. Questions: (a)Find P(-z_0.025 < Z < z_0.025) (b)Find P(-z_alpha/2 < Z < 2_alpha/2). (c)Find the value of z_alpha (rounded to 3 decimals) such that P(Z > z_alpha) = 0.05.
Mathematics
1 answer:
Reptile [31]3 years ago
6 0

Answer:

a) P(-z_0.025 < Z < z_0.025)

For this case we want a quantile that accumulates 0.025 of the area on the tails of the normal standard distribution, and for this case we can calculate the z value with the following excel codes:

"=NORM.INV(0.025,0,1)"

"=NORM.INV(0.025,0,1)"

And for this case the two values are :z_{crit}= \pm 1.96

b) P(-z_{\alpha/2} < Z < z_{\alpha/2})

For this case we want a quantile that accumulates \alpha/2 of the area on the tails of the normal standard distribution, and for this case we can calculate the z value with the following excel codes:

"=NORM.INV(alpha/2,0,1)"

"=NORM.INV(alpha/2,0,1)"

c) For this case we want to find a value of z that satisfy:

P(Z > z_alpha) = 0.05.

And we can use the following excel code:

"=NORM.INV(0.95,0,1)"

And we got z_{\alpha/2}=1.64

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Part a

P(-z_0.025 < Z < z_0.025)

For this case we want a quantile that accumulates 0.025 of the area on the tails of the normal standard distribution, and for this case we can calculate the z value with the following excel codes:

"=NORM.INV(0.025,0,1)"

"=NORM.INV(0.025,0,1)"

And for this case the two values are :z_{crit}= \pm 1.96

Part b

P(-z_{\alpha/2} < Z < z_{\alpha/2})

For this case we want a quantile that accumulates \alpha/2 of the area on the tails of the normal standard distribution, and for this case we can calculate the z value with the following excel codes:

"=NORM.INV(alpha/2,0,1)"

"=NORM.INV(alpha/2,0,1)"

Part c

For this case we want to find a value of z that satisfy:

P(Z > z_alpha) = 0.05.

And we can use the following excel code:

"=NORM.INV(0.95,0,1)"

And we got z_{\alpha/2}=1.64

You might be interested in
Find the coordinates of the midpoint of a segment with the given endpoints.
Arada [10]
1. x midpoint: (-9+4)/(2) = -2
2. y midpoint: (3+7)/(2) = 5
3. The midpoint is (-2,5)
5 0
3 years ago
Read 2 more answers
The 20 girls in the class represented 55% of the students in the class. How many students are in the class?
inna [77]

Answer:

There are 31 students in the class.

Step-by-step explanation:

4 0
3 years ago
Solve the following system for y: 2x – 15y = –10 –4x + 5y = –30
Mamont248 [21]
Y=x-10/5 hope i help
4 0
3 years ago
Solve the equation. -4(7x + 8) = 192​
AleksAgata [21]
-8 is the answer ........
7 0
3 years ago
Factor the following:<br><br> 1. 5(a+3)²- (a+3<br><br> 2. p²- 6 - q · (p²- 6)²
scoundrel [369]

Answer:

1. (a + 3)(5a-14)

2. (p^2-6)[1-q(p^2-6)]

Step-by-step explanation:

1. The first thing to do to factor the expression is to take the expression (a + 3) as a common factor with its lowest exponent.

Then the expression. 5(a + 3)^2- (a + 3) remains as:

(a + 3)(5 (a + 3) -1)\\\\(a + 3)(5a +15 -1)\\\\(a + 3)(5a-14)

2. The first thing to do to factor the expression is to take the expression  p^2 -6 as its common factor with its lowest exponent.

Then the expression p^2- 6 - q(p^2- 6)^2 remains as:

(p^2-6)[1-q (p^2-6)]

8 0
3 years ago
Other questions:
  • 2.394inches per minute about how many inches will it travel in 7.489minutes.
    12·2 answers
  • What is the degree of EMD and what is the degree for DMB
    15·1 answer
  • Evaluate 7+(-4×^2)for ×=0
    15·1 answer
  • HELP MEH PLEASE! THIS IS HALF MY GRADE! Subtract 16a+3 from 13a−5 . Which is the correct answer?
    9·1 answer
  • Need help in this mathquestion. The function h(x)=(x+2)^2 can be expressed in the form f(g(x)) where f(x)=x^2 , and g(x) is defi
    7·1 answer
  • The total cost of renting a lawn mower from Lawns Inc. is represented by the function y = 10x + 15, where x represents the numbe
    12·1 answer
  • great rapids white water rafting company rents for $125 per hour. Explain why the point (0,0) and (1,125) are on the graph of th
    7·2 answers
  • Plz help me i really need this down i will give a 100 if u answer it right
    11·2 answers
  • Find the radius of a circle with a circumference of 18.58 feet
    12·1 answer
  • In science class, the average score on a lab report is 82 points, with all students scoring within 3.2 points of the average. If
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!