Question

Weekly wages at a certain factory are normally distributed with a mean of $400 and a standard deviation of $50. Find the probability that a worker selected at random makes between $450 and $550.

Answer 1

To find the probability that a worker selected at random makes between $450 and $550, we need to calculate the area under the normal distribution curve between those two values.

Step-by-step explanation:

To find the probability that a worker selected at random makes between $450 and $550, we need to calculate the area under the normal distribution curve between those two values. First, we convert the values to z-scores using the formula: z = (X - mean) / standard deviation. For $450: z1 = (450 - 400) / 50 = 1. For $550: z2 = (550 - 400) / 50 = 3. Next, we find the cumulative probability for each z-score using a standard normal distribution table or calculator. P(1 <= z <= 3) is equal to P(z <= 3) - P(z <= 1). Finally, we look up the cumulative probabilities in the standard normal distribution table or use a calculator to find the probabilities.