Answer:
0.6844 = 68.44% probability that a drum meets the guarantee.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Mean of 101.8 pounds and a standard deviation of 3.76 pounds.
This means that
What is the probability that a drum meets the guarantee?
Probability of at least 100 lbs of solvent, which is 1 subtracted by the p-value of Z when X = 100. So
has a p-value of 0.3156.
1 - 0.3156 = 0.6844
0.6844 = 68.44% probability that a drum meets the guarantee.