Question

The budget for a window display can be modeled by an approximately normal distribution with a mean of $500 and a standard deviation of $80. Calculate the window display budget (in dollars) representing the bottom 15% of all window display budgets. (Use a table or technology. Round your answer to two decimal places.)

Answer 1

Given that,

mean = $\mu$ = $500

standard deviation = $\sigma$ = $80

Using standard normal table,

P(Z < z) = 15%

= P(Z < z) = 0.15  

= P(Z <- 1.04 ) = 0.15

z = - 1.04 Using standard normal table,

Using z-score formula  

x= z * $\sigma$ + $\mu$

x=- 1.04 *80+500

x= 416.80