Question

During the past six months, 73.2 percent of U.S. households purchased sugar. Assume that these expenditures are approximately normally distributed with a mean of $8.22 and a standard deviation of $1.10. Find the probability that a household spent less than $5.00 on sugar.

Answer 1

0.0017 is the probability that a household spent less than $5.00 on sugar.

Explanation:

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = $8.22

Standard Deviation, σ = $1.10

We are given that the distribution of expenditure is a bell shaped distribution that is a normal distribution.

Formula:

`z_(score) = \displaystyle(x-\mu)/(\sigma)`

P( household spent less than $5.00 on sugar)

P(x < 5)

`P( x< 5) = P( z < \displaystyle(5 - 8.22)/(1.10)) = P(z < -2.9272)`

Calculation the value from standard normal z table, we have,

`P(x < 5) = 0.0017`

0.0017 is the probability that a household spent less than $5.00 on sugar.