Using the normal distribution, the probability that a worker selected at random makes between $500 and $550 is: 2.15%.
Normal Probability Distribution
The z-score of a measure X of a normally distributed variable with mean mu and standard deviation sigma is given by:
Z = (X - mu)/sigma
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
The mean and the standard deviation are given as follows:
mu = 400, sigma = 50
The probability is the p-value of Z when X = 550 subtracted by the p-value of Z when X = 500, hence:
X = 550:
Z = (X - mu)/sigma
Z = (550 - 400)/50
Z = 3
Z = 3 has a p-value of 0.9987.
X = 500:
Z = (X - mu)/sigma
Z = (500 - 400)/50
Z = 2
Z = 2 has a p-value of 0.9772.
0.9987 - 0.9772 = 0.0215 = 2.15% probability.
More can be learned about the normal distribution at https://brainly.com/question/15181104
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