Question

Keystone is curious how likely they are to reach their annual revenue target. Past experience suggests that annual revenue follows a typical bell-shaped distribution, with a mean of $32 million and a standard deviation of $4 million. Keystone has set a revenue goal of $35 million for this year. How likely are they to reach the target based on the historical data? In order to remain in good standing with investors, Keystone needs to make at least $26 million. What are the chances they fail fall into poor standing with their investors?

Answer 1

Given,

Probability that the keystone meets the revenue target of $35 million is,

P(x > 35) is,

z = (35 - 32)/4 = 0.75

P(z > 0.75) = 0.2276

Therefore, there is 22.76% chance that they will meet the target revenue of $35 million

Keystone needs to make at least $26 million for good standing,

z = (26 - 32)/4 = -1.5

P(x > 26) = P(z > -1.5) = 0.9332

The chances that they fail to fall into poor standing with their investors is 93.32%