Question

HELPPPP

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

Answer 1

13.5

Explanation:

Answer 2

0.13591 = 13.59%.

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.

`z=(x-\mu)/(\sigma)`, where,

`z=\text{z-score}`,

`x=\text{Sample-score}`,

`\mu=\text{Mean}`,

`\sigma=\text{Standard deviation}`.

`z=(450-400)/(50)`

`z=(50)/(50)`

`z=1`

Let us find z-score for sample score 500.

`z=(500-400)/(50)`

`z=(100)/(50)`

`z=2`

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

`P(z<1)=0.84134`

`P(z<2)=0.97725`

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

`P(1<z<2)=P(z<2)-P(z<1)`

Upon substituting our values we will get,

`P(1<z<2)=0.97725-0.84134`

`P(1<z<2)=0.13591`

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