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soldier1979 [14.2K]
2 years ago
14

According to the empirical (69-95-99.7) rule, if a random variable z has a standard normal distribution, then approximately 95%

Mathematics
1 answer:
Dmitry_Shevchenko [17]2 years ago
7 0

Using z-scores, it is found that the value of z is z = 1.96.

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

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula, which for a measure X, in a distribution with mean \mu and standard deviation \sigma, is given by:  

Z = \frac{X - \mu}{\sigma}

  • It measures how many standard deviations the measure is from the mean.
  • Each z-score has an associated p-value, which is the percentile.

  • The normal distribution is symmetric, which means that the middle 95% is between the <u>2.5th percentile and the 97.5th percentile</u>.
  • The 2.5th percentile is Z with a p-value of 0.025, thus Z = -1.96.
  • The 97.5th percentile is Z with a p-value of 0.975, thus Z = 1.96.
  • Thus, the value of Z is 1.96.

A similar problem is given at brainly.com/question/16965597

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A and B can fill a cistern in 4 hours. A and C can fill
kirill [66]

Answer:

20 hours

Step-by-step explanation:

We can work easier if we think in terms of an hour

the first equation that we can write is

A + B = 1/4 (its meaning is that in an hour A and B fill 1/4 of the cistern)

the second equation we can write is

A + C = 1/5 (its meaning is that in an hour A and C fill 1/5 of the cistern)

the third equation that we can write is

B = 2C  (its meaning is that in an hour B fill 2 times C the cistern)

now we can substitute the value of B in the first two equations

A + 2C = 1/4

A + C = 1/5

A = 1/5 - C

1/5 - C + 2C = 1/4

C = 1/4 -1/5

C = (5-4)/20

C = 1/20 (this means that in an hour C will fill 1/20 of the cistern, so it takes 20 hours to fill the entire cistern)

A = 1/5 - 1/20

A = (4-1)/20 = 3/20

B = 1/20 *2 = 1/10

4 0
2 years ago
What is the solution of (3x + 8)/(x - 4) &gt;= 02
ipn [44]

Answer:

3x+8=0

x=-8/3The face of the denominator must be 0

And the face and denominator of the fraction must be positive

Step-by-step explanation:

4 0
2 years ago
if a 12 sides regular polygon rotates about it’s center at which angle of rotation will the image of the polygon coincide with t
kotegsom [21]

360 / 12 = 30

So, it's 30 degrees.


Incidentally, a 12 sided polygon is called a dodecagon.



6 0
2 years ago
Read 2 more answers
How can distributive property be used to solve 7 x 391
Advocard [28]

Answer:

7x ³⁹¹

Step-by-step explanation:

1: "x3" was replaced by "x^3".

7 0
2 years ago
Solve for x. Write the smaller solution first, and the larger solution second. (2x-1)(x+4)=0 smallerX- largerX-
Vilka [71]

Answer:

Two solutions were found :

x = -4

x = 1/2 = 0.500

Step-by-step explanation:

Step  1  :

Equation at the end of step  1  :

 (2x - 1) • (x + 4)  = 0

Step  2  :

Theory - Roots of a product :

2.1    A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

2.2      Solve  :    2x-1 = 0

Add  1  to both sides of the equation :

                     2x = 1

Divide both sides of the equation by 2:

                    x = 1/2 = 0.500

Solving a Single Variable Equation :

2.3      Solve  :    x+4 = 0

Subtract  4  from both sides of the equation :

                     x = -4

Two solutions were found :

x = -4

x = 1/2 = 0.500

Processing ends successfully

plz mark me as brainliest :)

8 0
3 years ago
Read 2 more answers
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