Question

For certain​ workers, the mean wage is ​$7​/hr, with a standard deviation of ​$.75 if a worker is chosen at​ random, what is the probability that the​ worker's wage is between ​$6.25 and ​$7.75​? assume a normal distribution of wages

Answer 1

The probability of a worker's wage falling between $6.25 and $7.75 is found by calculating the z-scores of these values, looking up the corresponding percentiles in a standard normal distribution, and subtracting the smaller percentile from the larger one.

Step-by-step explanation:

To calculate the probability that a randomly chosen worker's wage is between $6.25 and $7.75, we first need to determine the z-scores for these wage values. The z-score is found by subtracting the mean from the value and then dividing by the standard deviation. For $6.25, the z-score is (6.25 - 7) / 0.75 = -1. For $7.75, the z-score is (7.75 - 7) / 0.75 = 1. We then look up these z-scores in a standard normal distribution table or use a calculator with a normal distribution function to find the probabilities.

The area between the z-scores represents the probability that a worker's wage falls in that range. For example, a z-score of -1 corresponds to the 15.87th percentile and a z-score of 1 corresponds to the 84.13th percentile in a standard normal distribution. The difference between these percentiles gives us the probability of a worker's wage falling between $6.25 and $7.75.