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#?

1 Answer
Shwetank Mauria
Jun 24, 2017

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%#

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