Answer:
The probability that a worker selected at random makes between $500 and $550 is approximately 0.24.
Explanation:
To calculate this probability, we can use the standard normal distribution, which is a normal distribution with a mean of 0 and a standard deviation of 1. We can convert the weekly wage amounts to standard units by subtracting the mean and dividing by the standard deviation.
For wages between $500 and $550, the corresponding standard units are:
$500 - $400 = $100 / $50 = 2
$550 - $400 = $150 / $50 = 3
We can use a standard normal table or a calculator to find the probability that a value chosen at random from the standard normal distribution falls within the range of 2 to 3 standard units. This probability is approximately 0.24.
Since the weekly wages at the factory are normally distributed with a mean of $400 and a standard deviation of $50, this probability is also the probability that a worker selected at random makes between $500 and $550.