Question

What is the probability of drawing a random sample of 21 ( N= 21) withx51.5 or smaller from a skewed (non-normal) population in which μ=55 and σ=18 ?

Answer 1

To find the probability of drawing a random sample of 21 ( N = 21) with x ≤ 51.5 from a skewed (non-normal) population with μ = 55 and σ = 18, you need to use the z-score formula and the standard normal distribution.

Step-by-step explanation:

To find the probability of drawing a random sample of 21 ( N = 21) with x ≤ 51.5 from a skewed (non-normal) population with μ = 55 and σ = 18, we need to use the z-score formula and the standard normal distribution.

The z-score formula is: z = (x - μ) / σ

1. Calculate the z-score for x = 51.5: z = (51.5 - 55) / 18 = -0.1944
2. Consult the standard normal distribution table or use a calculator to find the cumulative probability for z = -0.1944. (Note: The standard normal distribution is assumed to be approximately normal for large sample sizes.)
3. The probability of drawing a random sample with x ≤ 51.5 is the cumulative probability obtained in the previous step. It represents the area under the standard normal curve to the left of -0.1944.

By following these steps, you can find the probability of drawing a random sample of 21 with x ≤ 51.5 from the given skewed population.