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

Answer:

d. 0.3446

Step-by-step explanation:

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

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

$z=\frac{x-\mu}{\sigma}$

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:

$z=\frac{1,000-1,100}{250}$

$z=\frac{-100}{250}$

$z=-0.4$

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.