Question

A population mean (u) of 5 and a standard deviation (o) of 2. if n=3, what proportion of the means of a sampling distribution would be less than 4.0?

a) 0.3078
b) 0.0668
c) 0.1922
d) 0.3085

Answer 1

To calculate the proportion of the means of a sampling distribution that would be less than 4.0, use the z-score formula.

Step-by-step explanation:

To calculate the proportion of the means of a sampling distribution that would be less than 4.0, we need to find the z-score for 4.0 using the formula:

z = (x - u) / (o / sqrt(n))

where x is the value we want to calculate the proportion for (4.0 in this case), u is the population mean (5), o is the standard deviation (2), and n is the sample size (3).

Plugging in the values, we get:

z = (4.0 - 5) / (2 / sqrt(3)) = -0.866

We can then use a standard normal distribution table to find the proportion associated with this z-score. The proportion is approximately 0.1932, which is closest to option c) 0.1922.