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

$80

Step-by-step explanation:

400÷50= 80 which is the weekly rate of wages

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%.

13.59%

Step-by-step explanation:

Calculate the z-scores.

z = (x − μ) / σ

z₁ = (450 − 400) / 50

z₁ = 1

z₂ = (500 − 400) / 50

z₂ = 2

Use a chart or calculator to find the probability.

P(1

= P(Z

= 0.9772 − 0.8413

= 0.1359

13.5

Step-by-step explanation:

Then, the probability yields, P(0.00 ≤ z ≤ 1.00) = 0.3413 - 0.0000 = 0.3413

Step-by-step explanation:

used the z thing to solve it