Answer:
41.94% probability that a worker earned between $400 and $500.
Step-by-step explanation:
Problems of normally distributed samples can be 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 is the probability that a worker earned between $400 and $500?
This is the pvalue of Z when X = 500 subtracted by the pvalue of Z when X = 400. So
X = 500
has a pvalue of 0.7422
X = 400
has a pvalue of 0.3228
So there is a 0.7422 - 0.3228 = 0.4194 = 41.94% probability that a worker earned between $400 and $500.