The lengths of human pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. what is the probability that a pregnancy last at least 300 days? round to four decimal places.

A. P(x>300)=0.0166

Step-by-step explanation:

A. The problem tell us we are working in a Normal Distribution with mean 268 and STD of 15, and we are asked for the probability that a pregnancy last at least 300 days. The probability is not meant to be found directly (it´s too difficult to find it in "that" distribution), there´s a process called "Normalize" which is used to transfer the problem from an specific Normal Distribution to a Standard Normal Distribution (with mean 0 and STD 1) where we are able to find probabilities easier as follows:

P(x<a)= P( (x-μ)/σ < (a-μ)/σ ) = P(z<b)

Where x,a,μ,σ are data in the specific Normal Distribution (a the value that we want its probability, μ the mean and σ the STD) and z,b are equivalent data to x,a but they are from a Standard Normal Distribution.

It´s useful to do this because in a Standard Normal Distribution we are able to find probabilities easier. A way to find those values, is to use a chart (it´s attached to this answer) with the probabilities that works like this:

P(z<b)= (u,v)

Where (u,v) are the coordinates of the value of the probability with u=whole part and first decimal of b, and v=second decimal of b. Keep in mind that it only works with probabilities UNDER a value ("<")

We will use this problem as an example.

First we write the probability we want and "Normalize" it:

P(x>300) = P( (x-μ)/σ > (300-268)/15 ) = P(z>2,133...)

But the chart only works with "<", so we rewrite it with a property of probability:

P(z>2,133...) = 1 - P(z<2,133...)

And now, we are able to look for the value of this probability:

P(z<2,1333...) = the place with coordinates (2,1  ,  4 (because it´s periodic))

P(z<2,1333...) =0.9834

P(z>2,133...) = 1 - 0.9834 = 0.0166

But we know P(x>300) = P(z>2,133...), so our answer will be:

P(x>300) = 0.0166

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

da freeck kinda math is this just drop out

step-by-step explanation: