DESCRIPTIVE STATISTICS

Question

A population of values has a normal distribution with μ=7.1 and σ=65.9. You intend to draw a random sample of size n=80.

Find the probability that a single randomly selected value is less than 27.7.

P(X < 27.7) = 

Find the probability that a sample of size n=80 is randomly selected with a mean less than 27.7.

P(M < 27.7) = 

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

List of provided parameters to take into consideration:

1. Sample Mean = 7.1
2. Population Standard Deviation = 65.9
3. Sample Size = 80

Based on the information imparted, we can appropriately utilize the Z-Score Equation to compute the probability:

Z = [27.7 - Sample Mean] / [Population Standard Deviation]

Z = [27.7 - 7.1] / [65.9]

Z = 0.313

P [x < 27.7] = P [Z < 0.313]

Utilizing the [+] Z-Score Table, P [Z < 0.313] = 0.6217

Based on the information imparted, we can appropriately utilize the Z-Score Equation to compute the probability:

Z = [27.7 - Sample Mean] / [(Population Standard Deviation) / Sqrt (Sample Size)]

Z = [27.7 - 7.1] / [(65.9) / Sqrt (80)]

Z = 2.80

P [x-Bar < 27.7] = P [Z < 2.80]

Utilizing the [+] Z-Score Table, P [Z < 2.80] = 0.9974