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.
250 300 350 400 450 500 550
P=[?]%
Hint use the 68-95-99.7 rule.
Enter

Answer 1

First, we need to standardize the values using the formula:

z = (x - mu) / sigma

where x is the value, mu is the mean, and sigma is the standard deviation.

For $450: z = (450 - 400) / 50 = 1

For $550: z = (550 - 400) / 50 = 3

Using the 68-95-99.7 rule, we know that approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

Since we are interested in the probability of a worker making between $450 and $550, we need to find the area under the normal curve between z = 1 and z = 3.

Using a standard normal table or calculator, we can find that the area under the curve between z = 1 and z = 3 is approximately 0.1359.

Therefore, the probability that a worker selected at random makes between $450 and $550 is 13.59% (rounded to two decimal places).

Explanation: