Answer:
c. binomial distribution with n = 5 and p = 1/33.
Step-by-step explanation:
For each birth, there are only two possible outcomes. Either it results in a defect, or it does not. The probability of a birth resulting in a defect is independent of other births. So we use the binomial probability distrbution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
![P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20C_%7Bn%2Cx%7D.p%5E%7Bx%7D.%281-p%29%5E%7Bn-x%7D)
In which
is the number of different combinations of x objects from a set of n elements, given by the following formula.
![C_{n,x} = \frac{n!}{x!(n-x)!}](https://tex.z-dn.net/?f=C_%7Bn%2Cx%7D%20%3D%20%5Cfrac%7Bn%21%7D%7Bx%21%28n-x%29%21%7D)
And p is the probability of X happening.
The proportion of American births that result in a birth defect is approximately 1/33 according to the Centers for Disease Control and Prevention (CDC).
This means that the probability of a birth resulting in a defect is ![p = \frac{1}{33}](https://tex.z-dn.net/?f=p%20%3D%20%5Cfrac%7B1%7D%7B33%7D)
A local hospital randomly selects five births.
This means that ![n = 5](https://tex.z-dn.net/?f=n%20%3D%205)
So the correct answer is:
c. binomial distribution with n = 5 and p = 1/33.
Answer:
65 degrees
Step-by-step explanation:
corresponding angles
Answer:
The coordinates of point P are (-1, -1)
Step-by-step explanation:
The coordinates of the partition point (x, y) of a line segment whose endpoints are (x1, y1) and (x2, y2) at ratio m: n are
- x =
![\frac{mx2+nx1}{m+n}](https://tex.z-dn.net/?f=%5Cfrac%7Bmx2%2Bnx1%7D%7Bm%2Bn%7D)
- y =
![\frac{my2+ny1}{m+n}](https://tex.z-dn.net/?f=%5Cfrac%7Bmy2%2Bny1%7D%7Bm%2Bn%7D)
∵ P partitions segment HS in a ratio 2: 3
∴ P = (x, y)
∴ m = 2 and n = 3
∵ H = (5, -9) and S = (-10, 11)
∴ x1 = 5 and x2 = -10
∴ y1 = -9 and y2 = 11
→ Substitute them in the rule above to find x and y
∵ x =
=
= ![\frac{-5}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B-5%7D%7B5%7D)
∴ x = -1
∵ y =
=
= ![\frac{-5}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B-5%7D%7B5%7D)
∴ y = -1
∴ The coordinates of point P are (-1, -1).