Given a normally distributed population of values with a mean of 76 and a standard deviation of 10 what is the probability that a value is 71 and 82
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 calculated.
To find the probability that a value falls within a certain range in a normally distributed population, we need to standardize the values and then use a z-table or a z-score calculator.
The standardization formula is:
Z = (X - μ) / σ
Where:
Z = z-score
X = value from the population
μ = mean of the population
σ = standard deviation of the population
First, let's calculate the z-score for 71:
Z1 = (71 - 76) / 10
= -0.5
Next, let's calculate the z-score for 82:
Z2 = (82 - 76) / 10
= 0.6
Now, using a z-table or a z-score calculator, we can find the probabilities associated with those z-scores.
For Z1 = -0.5, the probability can be found by looking up the z-score in the table or using a z-score calculator. Let's assume the probability is P1.
For Z2 = 0.6, the probability can also be found by looking up the z-score in the table or using a z-score calculator. Let's assume the probability is P2.
The probability of a value falling between 71 and 82 is equal to the difference between P1 and P2:
P = P2 - P1
By finding the corresponding probabilities for the z-scores (-0.5 and 0.6) using a z-table or a z-score calculator, you can determine the probability that a value from the normally distributed population falls between 71 and 82.