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
1. What is the solution to the system below?<br> x+y=5<br> 1x- y=3
Alika [10]

Answer:

(4,1)

Step-by-step explanation:

x+y=5

x- y=3

Add the equations together to eliminate y

x+y=5

x- y=3

--------------------

2x = 8

Divide each side by 2

2x/2 = 8/2

x = 4

Now we can find y

x+y = 5

4+y = 5

Subtract 4 from each side

4+y-4 = 5-4

y =1

5 0
3 years ago
HELPP QUICK PLSSS The solution to a two-variable system is the point on a graph at which the lines cross
natali 33 [55]

Answer:

b. false, i think!

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
92.96 as a fraction
nikklg [1K]
To change a decimal to a fraction you need to first place the decimal over 1. Next, for each number behind the decimal, you will multiply by a multiple of 10. Since there are 2 numbers behind the decimal, it's 100. Therefore, 
92.96 x 100 = 9296
1 x 100= 100


Your new fraction is 9296/100. Now we simplify it. I'm going by 2's so it may take a bit. 
Simplifying it twice by 2's your answer would be:

2324/25


3 0
3 years ago
How to find vertex form with vertex: (3,6) and y intercept: 2
bekas [8.4K]

Answer:

<h3>              f(x) = - ⁴/₉(x - 3)² + 6</h3>

Step-by-step explanation:

The vertex form of  the equation of the parabola with vertex (h, k)  is:

f(x) = a(x - h)² + k

So for vertex (3, 6) it will be:

f(x) = a(x - 3)² + 6

<u>y intercept: 2</u> means  f(0) = 2

f(0) = a(0 - 3)² + 6

2 = a(-3)² + 6

2 -6 = 9a + 6 -6

-4 = 9a

a = ⁻⁴/₉

Therefore:

The vertex form of quardatic function with vertex: (3,6) and y intercept: 2 is

                             <u>f(x) = - ⁴/₉(x - 3)² + 6</u>

5 0
3 years ago
Select the term that best describes the statement if a polygon has eight sides then it is an octagon
Brut [27]
The answer you are looking for is "conditional".
5 0
3 years ago
Read 2 more answers
Other questions:
  • Write each mixed number as a whole number or decimal. classify each number according to the group(s) to which it belongs: ration
    9·1 answer
  • Write the following decimal as a fraction in simplest form 45/100
    7·1 answer
  • How to find all real solutions
    9·1 answer
  • The line has a slope of -3 and passes through the point 1,4
    5·2 answers
  • Which will help you answer, "To what power must a student raise the number 5 to have an answer of 625?"
    7·1 answer
  • Jonathan increased his rate of walking by 25% at halfway to his destination and therefore arrived half an hour earlier than was
    7·1 answer
  • The number of children in each family on a particular city block is shown in the dot plot:
    5·1 answer
  • ¿CUAL ES LA RAIZ CUADRADA DE 8362?
    10·1 answer
  • Write the inequality graphed on the number line.<br><br> -3 3
    13·1 answer
  • If you invest $100 at an interest rate of 6%, how much money will you have after two years?
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!