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Answer:
a)
b) 38.49% of the population is between 19 and 25.
c) 34.46% of the population is less than 17.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by
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. If we need to find the probability that the measure is larger than X, it is 1 subtracted by this pvalue.
For this problem, we have that
A normal population has a mean of 19 and a standard deviation of 5, so .
(a) Compute the z value associated with 25
This is Z when
(b) What proportion of the population is between 19 and 25?
This is the pvalue of Z when subtracted by the pvalue of Z when
.
X = 25 has , that has a pvalue of 0.8849.
X = 19 has , that has a pvalue of 0.5000.
So 0.8849-0.500 = 0.3849 = 38.49% of the population is between 19 and 25.
(c) What proportion of the population is less than 17?
This is the pvalue of Z when
has a pvalue of 0.3446.
This means that 34.46% of the population is less than 17.