If mean profits of an SME (small or medium enterprise) is #£46,000# and standard deviation is #£19,000#, what is the probability that a specific SME has profit between #£44,000# and #£48,000#?

1 Answer
Jun 25, 2017

The probability that a specific SME will have a profit between #£44,000# and #£48,000# is #2xx0.1053=0.2106# or #21.06%#

Explanation:

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

the #z#-score for #£44,000# is #(44000-46000)/19000=-0.1053#

and #z#-score for #£48,000# is #(48000-46000)/19000=0.1053#

From tables the probability between #z=-0.1053# and #z=0# is #0.0419#

and as normal distribution is symmetric and probability between #z=0# and #z=0.1053# too is #0.0419#

and the probability that a specific SME will have a profit between #£44,000# and #£48,000# is #2xx0.1053=0.2106# or #21.06%#

Note for #z=0.10#, we have #0.0398# and for #z=0.11#, we have #0.0438# andhence for #z=0.1053# we have #0.0398+(0.0438-0.0398)xx53/100=0.0398+0.0021=0.0419#