Consider random samples of size 50 from a population with proportion 0.15

Find the mean and standard error of the distribution of sample proportions.

Round your answer for the mean to two decimal places, and your answer for the standard error to three decimal places.

mean =

Standard error =

Is the sample size large enough for the Central Limit Theorem to apply? yes or no

a) Mean = 0.75

b) Standard error = 0.051

c) Yes                              

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 50

Sample proportion , p = 0.15

a) Mean

b) Standard error

c) Application of central limit theorem

Since the sample size is larger than 30, we cam apply central limit theorem for normal approximation.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1