Question

Suppose that the average annual revenue of a small business is $150,000 with a standard deviation of $40,000.

Assume that the revenue distribution is normal.

4. What is the probability that one business selected at random makes less than $120,000?

5. What is the probability that the average annual revenue of a random sample of 4 businesses is less than $120,000?

6. Why are your answers to the previous two questions different?

Answer 1

This is a normal distribution question with

P(x < 120000.0)=?
The z-score at x = 120000.0 is,

z = -0.75
This implies that

This is a normal distribution question with

Sample size (n) = 4
Since we know that

P(x < 120000.0)=?
The z-score at x = 120000.0 is,

z = -1.5
This implies that
P(x < 120000.0) = P(z < -1.5) = \textbf{0.0668}
PS: you have to refer z score table to find the final probabilities.

6. to find average of the sample, our standard deviation changes for this. so our answer for two question is different
Please hit thumbs up if the answer helped you