Answer:
5.77% probability that their mean systolic blood pressure is between 119 and 122.
Explanation:
The Central Limit Theorem estabilishes that, for a random variable X, with mean
and standard deviation
, a large sample size can be approximated to a normal distribution with mean
and standard deviation
.
Normal probability distribution
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:

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 problem, we have that:

Find the probability that their mean systolic blood pressure is between 119 and 122.
This is the pvalue of Z when X = 122 subtracted by the pvalue of Z when X = 119. So
X = 122



has a pvalue of 0.9959
X = 119



has a pvalue of 0.9382
So there is a 0.9959 - 0.9382 = 0.0577 = 5.77% probability that their mean systolic blood pressure is between 119 and 122.