Using the normal distribution, it is found that the probability that the sample mean is above 80 is of 0.1056 = 10.56%.
<h3>Normal Probability Distribution</h3>
The z-score of a measure X of a normally distributed variable with mean and standard deviation is given by:
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
- By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation .
The parameters are given as follows:
.
The probability that the sample mean is above 80 is <u>one subtracted by the p-value of Z when X = 80</u>, hence:
By the Central Limit Theorem
Z = 1.25
Z = 1.25 has a p-value of 0.8944.
1 - 0.8944 = 0.1056.
0.1056 = 10.56% probability that the sample mean is greater than 80.
More can be learned about the normal distribution at brainly.com/question/4079902
#SPJ1