Answer:
The mean of this distribution is 36 years.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
There is a 0.02275 probability that the age of any randomly chosen person in the department is less than 22
This means that when X = 22, Z has a pvalue of 0.02275. So when X = 22, Z = -2. So
The mean of this distribution is 36 years.