Answer:
d. 2.28%
Step-by-step explanation:
Problems of normally distributed samples are 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 percentage of bolts will have a diameter greater than 0.32 inches?
This is 1 subtracted by the pvalue of Z when X = 0.32. So
has a pvalue of 0.9772
1 - 0.9772 = 0.0228 = 2.28%
So the correct answer is:
d. 2.28%