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
natta225 [31]
3 years ago
14

Assume that X is normally distributed with a mean of 20 and a standard deviation of 2. Determine the following. (a) P(X 24) (b)

P(X 18) (c) P(18 X 22) (d) P(14 X 26) (e) P(16 X 20) (f) P(20 X 26)
Mathematics
1 answer:
Tems11 [23]3 years ago
8 0

Answer:

a) P( X < 24 ) =  0.9772

b) P ( X > 18 ) =0.8413

c) P ( 14 < X < 26) = 0.9973

d)  P ( 14 < X < 26)  = 0.9973

e) P ( 16 < X < 20)  = 0.4772

f) P ( 20 < X < 26)  =  0.4987

Step-by-step explanation:

Given:

- Mean of the distribution u = 20

- standard deviation sigma = 2

Find:

a. P ( X  < 24 )

b. P ( X  > 18 )

c. P ( 18 < X  < 22 )

d. P ( 14 < X  < 26 )

e. P ( 16 < X  < 20 )

f. P ( 20 < X  < 26 )

Solution:

- We will declare a random variable X that follows a normal distribution

                                   X ~ N ( 20 , 2 )

- After defining our variable X follows a normal distribution. We can compute the probabilities as follows:

a) P ( X < 24 ) ?

- Compute the Z-score value as follows:

                                   Z = (24 - 20) / 2 = 2

- Now use the Z-score tables and look for z = 2:

                                   P( X < 24 ) = P ( Z < 2) = 0.9772

b) P ( X > 18 ) ?

- Compute the Z-score values as follows:

                                   Z = (18 - 20) / 2 = -1

- Now use the Z-score tables and look for Z = -1:

                    P ( X > 18 ) = P ( Z > -1) = 0.8413

c) P ( 18 < X < 22) ?

- Compute the Z-score values as follows:

                                   Z = (18 - 20) / 2 = -1

                                   Z = (22 - 20) / 2 = 1

- Now use the Z-score tables and look for z = -1 and z = 1:

                   P ( 18 < X < 22)  = P ( -1 < Z < 1) = 0.6827

d) P ( 14 < X < 26) ?

- Compute the Z-score values as follows:

                                   Z = (14 - 20) / 2 = -3

                                   Z = (26 - 20) / 2 = 3

- Now use the Z-score tables and look for z = -3 and z = 3:

                   P ( 14 < X < 26)  = P ( -3 < Z < 3) = 0.9973

e) P ( 16 < X < 20) ?

- Compute the Z-score values as follows:

                                   Z = (16 - 20) / 2 = -2

                                   Z = (20 - 20) / 2 = 0

- Now use the Z-score tables and look for z = -2 and z = 0:

                   P ( 16 < X < 20)  = P ( -2 < Z < 0) = 0.4772

f) P ( 20 < X < 26) ?

- Compute the Z-score values as follows:

                                   Z = (26 - 20) / 2 = 3

                                   Z = (20 - 20) / 2 = 0

- Now use the Z-score tables and look for z = 0 and z = 3:

                   P ( 20 < X < 26)  = P ( 0 < Z < 3) = 0.4987

You might be interested in
Use the diagram of the parallelogram to find the length of side PL and the measure of angle R.
Oxana [17]
The explanation is in a file the other Pearson put
4 0
3 years ago
Read 2 more answers
In an experiment, the one variable that is changed by the person doing the experiment is called the Question 2 options: controll
Ad libitum [116K]

Answer: Independent Variable

Step-by-step explanation:

The independent (or manipulated) variable is something that the experimenter purposely changes or varies over the course of the investigation. The dependent (or responding) variable is the one that is observed and likely changes in response to the independent variable.

5 0
3 years ago
Fill in the 3 blank boxes
Ket [755]
First one is 1 x 10^6
second is 2 x 10^8
third one is 157 times
6 0
3 years ago
What cryptographic method, first proposed in the mid-1980s, makes use of sloping curves instead of large prime numbers?
bearhunter [10]

Answer:

waffaafa

Step-by-step explanation:

awfafafafafaf

4 0
3 years ago
A car originally worth $32,000 is now worth only $14,000. By how much did the car depreciate?
yuradex [85]

Answer:

18,000 because 32+14=18

3 0
2 years ago
Read 2 more answers
Other questions:
  • How do you write 1÷3 as a fraction
    5·2 answers
  • According to a study done by De Anza students, the height for Asian adult males is normally distributed with an average of 66 in
    9·1 answer
  • In AFGH, h = 9.6 inches, f = 2.5 inches and 2G=78°. Find the length of g, to the
    8·1 answer
  • Evaluate -d - euf-g if d = 5, e = -6, f = 7 and g = -9<br> -27<br> 27<br> - 17<br><br> 17
    6·1 answer
  • The cost table shows the average cost, a(x), of
    5·2 answers
  • Celia is scheduled to work a total of 20 hours this week. So far she has worked
    11·1 answer
  • Need help with this asap!!
    12·1 answer
  • -3 5/12 divided 2 please help
    5·1 answer
  • If f(x) = -x-2, what is /(x)?
    13·1 answer
  • Suppose a car uses one gallon of gasoline for every 20 miles traveled.
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!