Answer:
94.52% probability that the random sample of 100 nontraditional students has a mean GPA greater than 3.42.
Step-by-step explanation:
Central Limit Theorem
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:
What is the probability that the random sample of 100 nontraditional students has a mean GPA greater than 3.42?
This is 1 subtracted by the pvalue of Z when X = 3.42.
has a pvalue of 0.0548.
So there is a 1-0.0548 = 0.9452 = 94.52% probability that the random sample of 100 nontraditional students has a mean GPA greater than 3.42.