A sample from a population with  = 40 and  = 10 has a mean of M = 44. If the sample mean corresponds to a z = 2.00, then how many scores are in the sample?

Question

A sample from a population with  = 40 and  = 10 has a mean of M = 44. If the sample mean corresponds to a z = 2.00, then how many scores are in the sample?

a. n = 100
b. n = 25
c. n = 5
d. n = 4

Answer 1

For this answer I got n=4 would this be right considering the numbers in the equation.

Answer 2

Well, let's see here. If the sample mean corresponds to a z-score of 2.00, that means our sample mean is 2 standard deviations above the population mean. And since the standard deviation is 10, that means our sample mean is 2 * 10 = 20 units above the population mean.

So, if our sample mean is 44 and it's 20 units above the population mean of 40, that means there must be 44 - 40 = 4 scores in the sample.

So the answer is d. n = 4.

But hey, don't worry! Four is not a clowning number. It's just a small sample size. Stick around for more jokes, though!

Answer 3

To determine the number of scores in the sample, we can use the formula for the z-score:

z = (X - μ) / (σ / √n)

Given that the mean of the population (μ) is 40, the standard deviation (σ) is 10, and the z-score is 2.00, we can rearrange the formula and solve for n:

2 = (44 - 40) / (10 / √n)

Simplifying the equation further:

2 = 4 / (10 / √n)

Multiplying both sides by (10 / √n):

2 * (10 / √n) = 4

Dividing by 2:

(10 / √n) = 2

Squaring both sides:

100 / n = 4

Simplifying the equation further:

n = 100 / 4

n = 25

Therefore, the number of scores in the sample is 25. Therefore, the correct answer is (b) n = 25.

Answer 4

To answer this question, we can use the formula for the standard score (z-score):

Z = (X - μ) / (σ / √n)

Here, Z is the given z-score (2.00), X is the sample mean (44), μ is the population mean (40), σ is the population standard deviation (10), and n is the number of scores in the sample (which we need to determine).

First, we can rearrange the formula to solve for n:

Z = (X - μ) / (σ / √n)

Multiply both sides of the equation by (σ / √n):

Z * (σ / √n) = (X - μ)

Divide both sides of the equation by Z:

(σ / √n) = (X - μ) / Z

Now, substitute the given values into the formula:

(10 / √n) = (44 - 40) / 2.00

Simplify the right side:

(10 / √n) = 4 / 2.00

Reduce:

(10 / √n) = 2

Now, we need to solve for n. To do this, square both sides of the equation:

(10 / √n)^2 = 2^2

10^2 / n = 4

100 / n = 4

Multiply both sides of the equation by n:

100 = 4n

Divide both sides of the equation by 4:

25 = n

Therefore, the number of scores in the sample is 25. Hence, the answer is b. n = 25.