The question is incomplete! Complete question along with answers and step by step explanation is provided below.
Question:
(a) Binomial probability distributions depend on the number of trials n of a binomial experiment and the probability of success p on each trial. Under what conditions is it appropriate to use a normal approximation to the binomial? (Select all that apply.)
nq > 10
np > 5
p > 0.5
np > 10
p < 0.5
nq > 5
(b) What is the probability of "12" or fewer successes for a binomial experiment with 20 trials. The probability of success on a single trial is 0.50. Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.)
Answer:
(a) The correct options are np > 5 and nq > 5
(b) P(x ≤ 12) = 0.8133
Step-by-step explanation:
Please refer to the attached images for explanation, I am unable to type in text editor due to some technical error!
- First, to shift the graph of
1 unit to the right, so ![y=x-1](https://tex.z-dn.net/?f=y%3Dx-1)
- Second, to shift the graph of
4 units to the left, so ![y=x-1+4](https://tex.z-dn.net/?f=y%3Dx-1%2B4)
<h2>
Explanation:</h2>
To translate the graph of a function is part of Rigid Transformations because the basic shape of the graph is unchanged
![Let \ c \ be \ a \ positive \ real \ number. \ \mathbf{Vertical \ and \ horizontal \ shifts} \\ in \ the \ graph \ of \ y=f(x) \ are \ represented \ as \ follows:](https://tex.z-dn.net/?f=Let%20%5C%20c%20%5C%20be%20%5C%20a%20%5C%20positive%20%5C%20real%20%5C%20number.%20%5C%20%5Cmathbf%7BVertical%20%5C%20and%20%5C%20horizontal%20%5C%20shifts%7D%20%5C%5C%20in%20%5C%20the%20%5C%20graph%20%5C%20of%20%5C%20y%3Df%28x%29%20%5C%20are%20%5C%20represented%20%5C%20as%20%5C%20follows%3A)
![\bullet \ Vertical \ shift \ c \ units \ \mathbf{upward}: \\ h(x)=f(x)+c \\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{downward}: \\ h(x)=f(x)-c](https://tex.z-dn.net/?f=%5Cbullet%20%5C%20Vertical%20%5C%20shift%20%5C%20c%20%5C%20units%20%5C%20%5Cmathbf%7Bupward%7D%3A%20%5C%5C%20h%28x%29%3Df%28x%29%2Bc%20%5C%5C%20%5C%5C%20%5Cbullet%20%5C%20Vertical%20%5C%20shift%20%5C%20c%20%5C%20units%20%5C%20%5Cmathbf%7Bdownward%7D%3A%20%5C%5C%20h%28x%29%3Df%28x%29-c)
![\bullet \ Horizontal \ shift \ c \ units \ to \ the \ right \ \mathbf{right}: \\ h(x)=f(x-c) \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ left \ \mathbf{left}: \\ h(x)=f(x+c)](https://tex.z-dn.net/?f=%5Cbullet%20%5C%20Horizontal%20%5C%20shift%20%5C%20c%20%5C%20units%20%5C%20to%20%5C%20the%20%5C%20right%20%5C%20%5Cmathbf%7Bright%7D%3A%20%5C%5C%20h%28x%29%3Df%28x-c%29%20%5C%5C%20%5C%5C%20%5Cbullet%20%5C%20Horizontal%20%5C%20shift%20%5C%20c%20%5C%20units%20%5C%20to%20%5C%20the%20%5C%20left%20%5C%20%5Cmathbf%7Bleft%7D%3A%20%5C%5C%20h%28x%29%3Df%28x%2Bc%29)
In this case, we have the graph of:
![y=x](https://tex.z-dn.net/?f=y%3Dx)
And we need to translate it to make it the graph of:
![y=x-1+4](https://tex.z-dn.net/?f=y%3Dx-1%2B4)
According to our rules we need:
- First, to shift the graph of
1 unit to the right, so ![y=x-1](https://tex.z-dn.net/?f=y%3Dx-1)
- Second, to shift the graph of
4 units to the left, so ![y=x-1+4](https://tex.z-dn.net/?f=y%3Dx-1%2B4)
But
is the same as
, so the previous steps can be simplified as:
- Shifting the graph of
3 unit to the left.
Below are shown those graphs:
- The blue one is
![y=x](https://tex.z-dn.net/?f=y%3Dx)
- The red one is
![y=x-1+4](https://tex.z-dn.net/?f=y%3Dx-1%2B4)
<h2>Learn more:</h2>
Shifting graphs: brainly.com/question/10010217
#LearnWithBrainly
Answer: 36
Step-by-step explanation:
A14 adaults 11 kids
Step-by-step explanation: