Question

A population of values has a normal distribution with μ=94μ=94 and σ=42.1σ=42.1. You intend to draw a random sample of size n=116n=116.

Find the probability that a single randomly selected value is between 87.4 and 90.5.
P(87.4 < X < 90.5) =

Find the probability that a sample of size n=116n=116 is randomly selected with a mean between 87.4 and 90.5.
P(87.4 < M < 90.5) =

Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Answer 1

Solution:

Find the probability that a single randomly selected value is between 87.4 and 90.5.
P(87.4 < X < 90.5) =0.0292

Find the probability that a sample of size n=116 is randomly selected with a mean between 87.4 and 90.5.
P(87.4 < M < 90.5) =0.1396

Explanation:

We are given:

Find the probability that a single randomly selected value is between 87.4 and 90.5.

Answer:

Using the z-score formula, we have:

Now using the standard normal distribution, we have:

Find the probability that a sample of size n=116 is randomly selected with a mean between 87.4 and 90.5.

Answer:

Using the z-score formula, we have:

Now using the standard normal distribution, we have: