Question

John Goodie is doing his budget. He discovers that he has spent an average of $235.00 a month on food for the year with a standard deviation of $55.00. What percent of his monthly expenses for this category would he expect to fall between $147.00 and $202.00?

Answer 1

He would expect his monthly expenses for food to fall between $147.00 and $202.00 with a probability of 21.95%

(the wording of the question should be something like "What percent would he expect his monthly expenses for this category to fall between $147.00 and $202.00?)

Step-by-step explanation:

Assume that his spending on food follows standard distribution

The probability that his expenses would be from 147.00 to 235.00 is given by f(z)

z = (235.00 - 147.00)/55 = 1.6 => f(z) = 0.4452 (44.52%)

(z is the z-score)

The probability that his expenses would be from 202.00 to 235.00 is given by f(z)

z = (235.00 - 202.00)/55 = 0.6 => f(z) = 0.2257 (22.57%)

So the probability that his expenses would be from $147.00 to $202.00 is

44.52% - 22.57% = 21.95%