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gayaneshka [121]
3 years ago
6

The annual rainfall (in inches) in a certain region is normally distributed with = 40 and = 4. What is the probability that star

ting with this year, it will take more than 10 years before a year occurs having a rainfall of more than 50 inches? What assumptions are you making?
Mathematics
1 answer:
sdas [7]3 years ago
3 0

Answer:

0.93970

Step-by-step explanation:

Solution:-

- Denote a random variable "X" The annual rainfall (in inches) in a certain region . The random variable follows a normal distribution with parameters mean ( μ ) and standard deviation ( σ ) as follows:

                          X ~ Norm ( μ , σ^2 )

                          X ~ Norm ( 40 , 4^2 ).

- The probability that it rains more than 50 inches in that certain region is defined by:

                          P ( X > 50 )

- We will standardize our test value and compute the Z-score:

                          P ( Z > ( x - μ )  / σ )

Where, x : The test value

                          P (  Z > ( 50 - 40 )  / 4 )

                          P (  Z > 2.5 )

- Then use the Z-standardize tables for the following probability:

                          P ( Z < 2.5 ) = 0.0062

Therefore,          P ( X > 50 ) = 0.0062

- The probability that it rains in a certain region above 50 inches annually. is defined by:

                           q = 0.0062 ,

- The probability that it rains in a certain region rains below 50 inches annually. is defined by:

                           1 - q = 0.9938

                           n = 10 years   ..... Sample of n years taken

- The random variable "Y" follows binomial distribution for the number of years t it takes to rain over 50 inches.

                          Y ~ Bin ( 0.9938 , 0.0062 )

- The probability that it takes t = 10 years for it to rain:

                         =  10C10* ( 0.9938 )^10 * ( 0.0062 )^0

                         = ( 0.9938 )^10

                         = 0.93970

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2 years ago
Which is the completely factored form of 4x2 28x 49? (x 7)(4x 7) 4(x 7)(x 7) (2x 7)(2x 7) 2(x 7)(x 7)
natima [27]

The completely factored form of 4x^2 + 28x + 49 is given by: Option C: (2x+7)(2x+7)

<h3>How to find the factors of a quadratic expression?</h3>

If the given quadratic expression is of the form ax^2 + bx + c, then its factored form is obtained by two numbers alpha( α ) and beta( β) such that:

b = \alpha + \beta \\ ac =\alpha \times \beta

Then writing b in terms of alpha and beta would help us getting common factors out.

Sometimes, it is not possible to find factors easily, so using the quadratic equation formula can help out without any  trial and error.

For this case, the given quadratic expression is:

4x^2 + 28x + 49

So we've to find two numbers such that:

Their sum = b =  28

Their product = ac = 4\times 49 = 196

We can see that 196 is square of 14, and that 14 added twice forms 28, thus:

14 + 14 = 28

14×14 = 196

Writing b = 28 as sum of 14 twice, we get:

4x^2 + 28x + 49 = 4x^2 + 14x + 14x +49 \\4x^2 + 28x + 49 =  2x(2x+7) + 7(2x + 7)\\4x^2 + 28x + 49  = (2x+7)(2x+7)

Thus, the completely factored form of 4x^2 + 28x + 49 is given by: Option C: (2x+7)(2x+7)

Learn more about factorization of quadratic expression here:

brainly.com/question/26675692

8 0
2 years ago
Jocelyn estimates that a piece of wood measures 5.5 cm. If it actually measures 5.62 cm, what is the percent error of Jocelyn's
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3 years ago
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Answer: B) 70.50

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3 0
2 years ago
The number X of days in the summer months that a construction crew cannot work because of the weather has the probability distri
Ronch [10]

Answer:

a.)The probability of losing no more than ten days next summer is    

    0.65

b.) The probability that 8 - 12 days will be lost next summer  is 0.8

c.)  The probability there will be no days lost next summer is 0.

Step-by-step explanation:

The probability distribution for the number X of days in the summer that a construction crew cannot work because of the weather is given below:

x                    P(x)

6                   0.03

7                   0.08

8                   0.15

9                   0.2

10                  0.19

11                   0.16

12                   0.1

13                   0.07

14                   0.02

a.) To find the probability that no more than 10 days will lost next summer can be found by adding the values of probability of the days lost which are 10 days or less, that is to say we can write

 

p( x ≤ 10 )  = p(x=6) + p(x =7) + p(x=8) + p(x=9) + p(x=10)

                = 0.03     + 0.08    + 0.15     + 0.2     + 0.19

                = 0.65

b.) To find the probability that 8 to 12 days will be lost next summer will be given by taking into account and adding the probabilities starting form the probability when 8 days are lost to the probability when 12 days are lost

   p( 8 ≤ x ≤ 12)  = p(x=8) + p(x=9) + p(x=10) + p(x=11) + p(x=12)

                          = 0.15 +    0.2     + 0.19    +   0.16  + 0.1

                          = 0.8

c.) The probability that no days will be lost next summer will be given by

    = 1 - ( p(x=6) + p(x=7) +  p(x=8) + p(x=9) + p(10) + p(11) + p(12))

    = 1 -  1

    = 0  

   The probability that will be no days lost next summer is zero. We can conclude that there will be some days lost next summer.

4 0
3 years ago
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