84.13% of the shipment is defective
Step-by-step explanation:
When the distribution is normal, we use 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.
Normally distributed with mean 39.3 and standard deviation 0.2
What percentage of the shipment is defective
Less than 39.5 or greater than 40.5.
Less than 39.5:
This is the pvalue of Z when X = 39.5. So
Greater than 40.5:
1 subtracted by the pvalue of Z when X = 40.5. So
1 - 1 = 0
Total:
0.8413 + 0 = 0.8413
84.13% of the shipment is defective