The Arc Electronic Company had an income of 90 million dollars last year. Suppose the mean income of firms in the same industry as Arc for a year is 75 million dollars with a standard deviation of 11 million dollars. If incomes for this industry are distributed normally, what is the probability that a randomly selected firm will earn more than Arc did last year? Round your answer to four decimal places.

0.0869

Step-by-step explanation:

The arc electronic company had an income of 90 million dollars last year.

Mean (μ) = 75 million dollars

Standard deviation (σ) = 11 million dollars

Probability that the randomly selected will earn more than arc did last year = Pr (x>90)

Using normal distribution,

Z = (x - μ) / σ

Z = (90 - 75) / 11

Z = 15/11

Z = 1.36

From the normal distribution table, 1.36 = 0.4131

Φ (z) = 0.4131

Recall that when Z is positive, Pr (x>a) = 0.5 - Φ (z)

= 0.5 - 0.4131

= 0.0869