Question

The prices of cell phone cases in a store are normally distributed.The mean of the prices is $22.90,and the standard deviation is $4.90.If you want to look at the bottom 45% of cases in terms of price,what is the cutoff price so that 45% of all cases are priced below that amount?

Answer 1

Given:

Mean = 22.90

Standard Deviation = 4.90

Find the cutoff price so that 45% of all cases are priced below that amount.

To solve this problem, the first thing we need to do is to find the z-score for 45% or 0.45.

The z-score for 0.45 is -0.126.

Now, to find the cutoff price or the "score", we will use the following equation

`z=(x-\mu)/(\sigma)`

Where:

z = z-score

x = score

μ = mean

σ = standard deviation

We are looking for the "x"

Derive the formula and substitute the given data.

`z=(x-\mu)/(\sigma)`
`\sigma z=x-\mu`
`x=z\sigma+\mu`
`x=(-0.126)(4.90)+22.90`
`x=22.28`

We got a value of 22.28 for our score, therefore, the cutoff price must be $22.28.