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