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 $500

0.13591 = 13.59%.

Step-by-step explanation:

We have been given that weekly wages at a certain factory are normally distributed with a mean of $400 and a standard deviation of $50.

First of all let us find the z-score for our given sample score using z-score formula.

, where,

,

,

,

.

Let us find z-score for sample score 500.

Let us find the probability of both z-score using normal distribution table.

Since we know that probability between two z-scores can be found by subtracting the smaller area from the larger area as:

Upon substituting our values we will get,

Therefore, the probability that a worker selected at random makes between $450 and $500 is 0.13591 or 13.59%.