Question

The profit of a small and medium enterprise (SME) has a mean of `£46,000` and standard deviation of `£19,000`. What is the probability that profit of a SME will be between `£40,000` and `£50,000`?

Answer 1

The probability that a specific SME will have a profit between `£40,000` and `£50,000` is `0.2073` or `20.73%`

Explanation:

As mean is `mu=£46,000` and standard deviation `sigma=£19,000`,

the `z`-score for `£40,000` is `(40000-46000)/19000=-0.3158`

and `z`-score for `£50,000` is `(50000-46000)/19000=0.2105`

From tables the probability between `z=-0.3158` and `z=0` is `0.1239`

and probability between `z=0` and `z=0.2105` is `0.0834`

Hence, the probability that a specific SME will have a profit between `£40,000` and `£50,000` is `0.1239+0.0834=0.2073` or `20.73%`