Answer: 0.0475
Step-by-step 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
[tex]\mu=\$50000[/tex] and [tex]\sigma=\$3000[/tex]
Let x be the random variable that represents the amount of money spent on red balloon.
Using formula [tex]z=\dfrac{x-\mu}{\sigma}[/tex], the z-score corresponding to x= 45000 will be :_
[tex]z=\dfrac{45000-50000}{3000}\approx-1.67[/tex]
Now, by using the standard normal distribution table for z, we have
P value : [tex]P(z<-1.67)=1-P(z<1.67)=1-0.9525=0.0475[/tex]
∴The proportion of home football game days in this town is less than $45000 worth of red balloons sold = 0.0475
