Question

Suppose the mean income of firms in the industry for a year is 95 million dollars with a standard deviation of 17 million dollars. If incomes for the industry are distributed normally, what is the probability that a randomly selected firm will earn less than 112 million dollars? Round your answer to four decimal places.

Answer 1

Given the mean income of firms in the industry for a year is 95 million dollars with a standard deviation of 17 million dollars. The incomes for the industry are distributed normally.

Let X be a random variable represents the income of the firm in the industry.

Hence,

We need to find the probability that a randomly selected firm will earn less than 112 million dollars i.e. P(X < 112).

Using the standard normal probability table,

0.8413 is the probability that a randomly selected firm will earn less than 112 million dollars.