a consumer survey indicates that the average household spends an average of $155 on groceries each week. The distribution of spending amounts is approximately normal with a standard deviation of$25. Based on this distribution.
a- what proportion of the population spends more then $175 dollars per week on groceries? b- what is the probability of randomly selecting a family that spends less than$100 per week on groceries?
c- how much money do you need yo spend on groceries watch week to be in the top 20% of the distribution?

2. Originally Posted by sf415415

a consumer survey indicates that the average household spends an average of $155 on groceries each week. The distribution of spending amounts is approximately normal with a standard deviation of$25. Based on this distribution.
a- what proportion of the population spends more then $175 dollars per week on groceries? b- what is the probability of randomly selecting a family that spends less than$100 per week on groceries?
c- how much money do you need yo spend on groceries watch week to be in the top 20% of the distribution?
(a) Calculate Pr(X > 175) = Pr( Z > 0.8) since $\displaystyle Z = \frac{x - \mu}{\sigma} = \frac{175 - 155}{25} = 0.8$.

Note that Pr(Z > 0.8) = 1 - Pr(Z < 0.8).

(b) Calculate Pr(X < 100).

(c) Find the value of a such that Pr(X > a) = 0.2.

To do this, find the value z* of Z such that Pr(Z > z*) = 0.2. Note that Pr(Z > z*) = 0.2 => Pr(Z < z*) = 0.8.

Then substitute z* ito $\displaystyle z* = \frac{a - 155}{25}$ and solve for a.