Question

If a one-person household spends an average of $52 per week on groceries, find the maximum and minimum amounts spent per week for the middle 50% of one-person households. Assume the standard deviation is $14 and the variable is normally distributed. Round your answers to the nearest hundredth.Minimum: $Maximum: $

Answer 1

For this case we have the following random variable:

X= amount spend on average for groceries by one person

And we have the following properties:

mean= 52

sd= 14

The distribution of the variable is normal

We can find the middle 50% using a graph like this one:

We can find two quantiles from the normal distribution that accumulates 25% of the area on each tail of the distribution and we have:

Z= -0.674 and 0.674

Now we can use the z score formula given by:

`z=(x-\mu)/(\sigma),x=\mu\pm z\cdot\sigma`

So then we have:

Minimum= 52 - 0.674*14 = 42.56

Minimum= 52 + 0.674*14 = 61.44