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STatiana [176]
3 years ago
11

The random variable X~(30,2^2) Find p(X<33) Find p(X>26)

Mathematics
1 answer:
Ostrovityanka [42]3 years ago
5 0

Answer:

i) P(X<33)  = 0.9232

ii) P(X>26) = 0.001

Step-by-step explanation:

<u><em>Step(i):-</em></u>

Given that the mean of the Population = 30

Given that the standard deviation of the Population = 4

Let 'X' be the Normal distribution

<u>Step(ii):-</u>

i)

Given that the random variable  X = 33

               Z = \frac{x-mean}{S.D}

               Z = \frac{33-30}{2} = 1.5 >0

P(X<33) = P( Z<1.5)

              = 1- P(Z>1.5)

             = 1 - ( 0.5 - A(1.5))

             = 0.5 + 0.4232

  P(X<33)  = 0.9232

<u>Step(iii) :-</u>

Given that the random variable  X = 26

               Z = \frac{x-mean}{S.D}

               Z = \frac{33-26}{2} = 3.5 >0

P(X>26)  = P( Z>3.5)

              = 0.5 - A(3.5)

              = 0.5 - 0.4990

             = 0.001

P(X>26) = 0.001

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valkas [14]

Answer: a) The customers surveyed purchased only mysteries =12

b) The customers purchased mysteries and science fiction​, but not romance novels=10

c) The customers purchased mysteries or science fiction=46

d) The customers purchased mysteries or science fiction​, but not romance novels=44

e) The customers purchased  exactly two types of​ books=21

Step-by-step explanation:

Given: n(S)=57

n(M)=33

n(S)=25

n(R)=18

n(M∩S)=12

n(R∩M)=9

n(S∩R)=6

n(R∩S∩M)=2

From the Venn diagram,

d=2

n(M∩S)=a+d=12

⇒a=10

n(R∩M)=b+d=9

⇒b=7

n(S∩R)=c+d=6

⇒c=4

Now, the customers surveyed purchased only mysteries=n(M)-a-b-d=33-10-7-4=12

The customers purchased mysteries and science fiction​, but not romance novels=a=10

The customers purchased mysteries or science fiction=n(M∪S)=n(M)+n(S)-n(M∩S)=33+25-12=46

The customers purchased mysteries or science fiction​, but not romance novels=n(M∪S)-d=46-2=44

The customers purchased  exactly two types of​ books= a+b+c=10+7+4=21

6 0
3 years ago
Write the standard form of a line that passes through (1, 1) and (3, 4)
Sophie [7]

Answer:

3x - 2y = 1

Step-by-step explanation:

Step 1:   Find the slope

slope m = (y2 - y1)(/x2 - x1)

 m = (4 - 1)/(3 - 1) = 3/2

Step 1:  Use the formula y = mx + b to solve

This is slope-intercept form of a line.  We have a slope of 3/2, and a point (x, y), which is (1, 1).  Plug those values into the equation above and solve for b (the only variable we are missing

1 = (3/2)(1) + b

   1 = 3/2 + b  

          1 - 3/2 = b

             2/2 - 3/2 = b

                  -1/2 = b

Step 2: Rewrite the formula using the slope and the b value we just calculated

 y = (3/2)x - 1/2

Step 3:  Standard form of a line is ax + by = c, where a is a positive integer, so we rearrange the equation from step 2 to standard form.  

y = (3/2)x - 1/2

 -(3/2)x + y = -1/2     (subtract (3/2)x from both sides)

 

      -3x + 2y = -1       (multiply by 2 to get rid of the fraction on x)

           3x - 2y = 1     (multiply by -1 so a becomes positive)    

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3 years ago
How many solutions does 3x – 1 = 3x + 1 have?
Ksju [112]
No solution. The terms cancel each other out!
5 0
3 years ago
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astra-53 [7]

Answer: 34%

Step-by-step explanation:

Given

Price is marked down by 60% with an additional discount of 15% on the marked down price

Suppose x is the original price of the item

After marking down, it is

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after additional discount it is

\Rightarrow 0.4x(1-0.15)=0.4x\times 0.85=0.34x

Effective discount on the item is

\Rightarrow \dfrac{x-0.34x}{x}\times 100=66\%

Thus, a person is paying 100-66=34\% of the original price

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yan [13]

Answer:

x=49750

Step-by-step explanation:

0.1(x + 250) = 5,000

Divide each side by .1

0.1(x + 250)/.1 = 5,000/.1

x+250 =50000

Subtract 250 from each side

x+250-250 = 50000-250

x=49750

3 0
3 years ago
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