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shutvik [7]
3 years ago
5

Let X be a normal random variable with mean 3 and variance 4. (a) Find the probability P(2 < X < 6). (b) Find the value c

such that P(X > c) = 0.33. (c) Find E[X2 ]. Hint: You can integrate with the density function, but it is quicker to relate E[X2 ] to the mean and variance.
Mathematics
1 answer:
Vanyuwa [196]3 years ago
4 0

Answer:

a) the probability of (2 < X < 6) is 0.6247

b) the value of c is 3.878

c) the value of E[ x² ] is 13

Step-by-step explanation:

Given that;

mean μ = 3

variance = 4

standard deviation s = √variance  = √4 = 2

(a) Find the probability P(2 < X < 6)

P(2 < X < 6) = p( (x - μ / s ) < z <  (x - μ / s ) )

= p( (2 - 3 / 2 ) < z < (6 - 3 / 2 ) )

= p( -0.5  < z <  1.5)

from z-score table, 1.5; z = 0.9332 and -0.5; z = 0.3085

so

P(2 < X < 6)  = 0.9332 - 0.3085 = 0.6247

Therefore, the probability of (2 < X < 6) is 0.6247

b) Find the value c such that P(X > c) = 0.33

with p-value = 0.33, the corresponding z -score to the right is 0.439

we know that;

z = x - μ / s

we substitute

0.439 = x - 3 / 2

x - 3 = 2 × 0.439

x - 3 = 0.878

x = 0.878 + 3

x = 3.878

Therefore, the value of c is 3.878

c) Find E[ x² ].

Variance = E[ x² ] - [ mean ]²

E[ x² ]  = Variance + [ mean ]²

we substitute

E[ x² ]  = 4 + [ 3 ]²

E[ x² ]  = 4 + 9

E[ x² ]  = 13

Therefore, the value of E[ x² ] is 13

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In the regular pentagon below, if AP = 4 m and BC = 10 m, find it's area.
12345 [234]

First symmetrically cut the pentagon to get 5 pieces. (So that you will get the idea that this polygon is divided into 5 triangles)

Then find the area of one of the triangles:

Area of Triangle = \frac{1}{2} bh

A = \frac{1}{2} × 4 × 10

A = 20 m²

To find the area of the whole pentagon shape:

A = 20 × 5 = 100 m²

<em>Hope it helps!</em>

4 0
2 years ago
the ratio of men to women at a class is 6 to 5 how many women students are there if there are 3600 men
torisob [31]
Ratio is 6:5
6+5=11

Men: 6 parts of 11 = 3600

6=3600
1=x
X=3600/6
=600.

Women: 5 parts of 11
1 part = 600
5 parts = 600x5
=3000
7 0
3 years ago
5x-9y-42=?(x+6)-9(y+?)
iren [92.7K]

Answer:

5 8

Step-by-step explanation:

Coefficient of x should be 5 so first ? should be 5 let the second ? = z

5×6-9×z=-42

30+42=9z

z=8

5 0
3 years ago
Read 2 more answers
The table shows the numbers y of students absent from school x days after a flu outbreak.
allsm [11]
  1. A function that models the data is given by this quadratic equation, y = -0.4908x² + 5.8845x + 1.3572.
  2. The number of students that are absent 10 days after the outbreak is equal to 11 students.

<h3>What is a scatter plot?</h3>

A scatter plot can be defined as a type of graph which is used for the graphical representation of the values of two (2) variables, with the resulting points showing any association (correlation) between the data set.

<h3>What is a quadratic function?</h3>

A quadratic function can be defined as a mathematical expression (equation) that can be used to define and represent the relationship that exists between two or more variable on a graph.

In Mathematics, the standard form of a quadratic equation is given by;

ax² + bx + c = 0

By critically observing the graph (see attachment) which models the data in the given table, we can infer and logically deduce that the quadratic function is given by:

y = -0.4908x² + 5.8845x + 1.3572

For the number of students that are absent 10 days after the outbreak, we have:

y = -0.4908(10)² + 5.8845(10) + 1.3572

y = -0.4908(100) + 58.845 + 1.3572

y = -49.08 + 58.845 + 1.3572

Number of students, y = 11.12 ≈ 11 students.

Read more on scatterplot here: brainly.com/question/6592115

#SPJ1

5 0
1 year ago
Help please? I can mark your answer as brainliest if you help :)
BlackZzzverrR [31]

Answer:The answer is D.

Step-by-step explanation:

7 0
2 years ago
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