Let X be the amount spent by a family of four on food per month.
The mean amount spent per month on food is μ = 500
The standard deviation σ =75
X follows Normal distribution with mean μ = 500 and standard deviation σ =75.
The probability that a family spends more than $410 per month is
P(x > 410) = [tex] P(\frac{x-mean}{standard deviation} > \frac{410 -500}{75} ) [/tex]
= P(z > -1.2)
= 1 - P(z < -1.2)
Using z score to find probability below -1.2
= 1 - 0.1151
P(x > 410) = 0.8849
The probability that a family spends more than $410 per month is 0.8849