True or False
If one score is randomly selected from a normal distribution with = 100 and = 20, the probability of obtaining a score between X = 80 and X = 120 is 0.3413.
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z scores.
Or you can go to http://davidmlane.com/hyperstat/z_table.html
False
To find the probability of obtaining a score between X = 80 and X = 120 from a normal distribution with a mean (μ) of 100 and a standard deviation (σ) of 20, we can use the Z-score formula and the standard normal distribution table.
The Z-score formula is given by:
Z = (X - μ) / σ
Let's calculate the Z-scores for X = 80 and X = 120:
Z1 = (80 - 100) / 20 = -1
Z2 = (120 - 100) / 20 = 1
Using the standard normal distribution table, we can find the probabilities associated with these Z-scores. Looking up the Z-scores in the table, we find that the probability of obtaining a Z-score of -1 is approximately 0.1587, and the probability of obtaining a Z-score of 1 is also approximately 0.1587.
To find the probability of obtaining a score between X = 80 and X = 120, we need to subtract the probability associated with the Z-score of -1 from the probability associated with the Z-score of 1:
P(-1 ≤ Z ≤ 1) = P(Z ≤ 1) - P(Z ≤ -1)
From the standard normal distribution table, we find that P(Z ≤ 1) is approximately 0.8413, and P(Z ≤ -1) is approximately 0.1587.
Therefore, the probability of obtaining a score between X = 80 and X = 120 is:
P(80 ≤ X ≤ 120) = 0.8413 - 0.1587 = 0.6826
So, the statement "the probability of obtaining a score between X = 80 and X = 120 is 0.3413" is FALSE. The correct probability is 0.6826.