Answer:
1. The minimum head breadth that will fit the clientele is of 3.95-in.
2. The maximum head breadth that will fit the clientele is of 9.25-in.
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 6.6-in and a standard deviation of 1.1-in.
This means that
1. What is the minimum head breadth that will fit the clientele?
The 0.8th percentile, which is X when Z has a p-value of 0.008, so X when Z = -2.41.
The minimum head breadth that will fit the clientele is of 3.95-in.
2. What is the maximum head breadth that will fit the clientele?
The 100 - 0.8 = 99.2nd percentile, which is X when Z has a p-value of 0.992, so X when Z = 2.41.
The maximum head breadth that will fit the clientele is of 9.25-in.