Answer:
Step-by-step explanation:
To find the probability that a worker selected at random makes between $350 and $500, we need to standardize the values and use the z-score formula.
First, we calculate the z-scores for $350 and $500:
Z_350 = ($350 - $400) / $50 = -1
Z_500 = ($500 - $400) / $50 = 2
Next, we look up the corresponding probabilities for the z-scores of -1 and 2 in the standard normal distribution (which follows the 68-95-99.7 rule):
For -1, the probability is approximately 0.1587.
For 2, the probability is approximately 0.9772.
To find the probability between $350 and $500, we subtract the probability of $350 from the probability of $500:
P($350 < w < $500) = P(Z < 2) - P(Z < -1) = 0.9772 - 0.1587 = 0.8185
Therefore, the probability that a worker selected at random makes between $350 and $500 is approximately 81.85%.
