Question

The amount of money spent on red balloon in a certain college town when the football team is in town is a normal random variable with mean $50000 and a standard deviation of $3000. What proportion of home football game days in this town is less than $45000 worth of red balloons sold?

Answer 1

Answer: 0.0475

Explanation:

Given : The amount of money spent on red balloon in a certain college town when the football team is in town is a normal random variable with

`\mu=\$50000` and
`\sigma=\$3000`

Let x be the random variable that represents the amount of money spent on red balloon.

Using formula
`z=(x-\mu)/(\sigma)`, the z-score corresponding to x= 45000 will be :_

`z=(45000-50000)/(3000)\approx-1.67`

Now, by using the standard normal distribution table for z, we have

P value :
`P(z<-1.67)=1-P(z<1.67)=1-0.9525=0.0475`

∴The proportion of home football game days in this town is less than $45000 worth of red balloons sold = 0.0475