Question

The weekly incomes of trainees at a local company are normally distributed with a mean of $1,100 and a standard deviation of $250. If a trainee is selected at random, what is the probability that he or she earns less than $1,000 a week?

Select one:
a. 0.8141
b. 0.1859
c. 0.6554
d. 0.3446

Answer 1

d. 0.3446

Explanation:

We need to calculate the z-score for the given weekly income.

We calculate the z-score of $1000 using the formula

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

From the question, the standard deviation is
`\sigma=250` dollars.

The average weekly income is
`\mu=1,100` dollars.

Let us substitute these values into the formula to obtain:

`z=(1,000-1,100)/(250)`

`z=(-100)/(250)`

`z=-0.4`

We now read from the standard normal distribution table the area that corresponds to a z-score of -0.4.

From the standard normal distribution table,
`Z_(-0.4)=0.34458`.

We round to 4 decimal places to obtain:
`Z_(-0.4)=0.3446`.

Therefore the probability that a trainee earns less than $1,000 a week is
`P(x\:<\:1000)=0.3446`.

The correct choice is D.