Question

A local high school requires every student fill out a survey for incoming students. After all 1,250 students finish the survey, the information is compiled and used to get population parameters for the student body. Student Council is deciding whether or not to add a soda vending machine to the cafeteria. Luckily one of the questions on the incoming survey was “On average, how many soft drinks do you drink each day?” Looking at all of the responses, they find that the average is 2.3 drinks per day with a standard deviation of 1.0 drinks.

a. To begin, the Student Council wants to know about how many students drink soda in general. How likely is it that a randomly chosen student drinks 1 soft drink or

more each day?

b.One of the members on the Student Council thinks that one vending machine won’t be enough. How likely is it that a randomly chosen student drinks more

than 3 soft drinks per day?

c.To get a second opinion, the Student Council randomly chooses 9 students and asks them how many soft drinks they drink each day. They get a sample average of 4.1

and want to know if this is typical. Knowing the population parameters, how likely was it that a sample of 9 students would have an average of 4.1 or more?

Answer 1

a) P(X > 1)

= P((X - )/> (1 - )/)

= P(Z ​​​​​> (1 - 2.3)/1)

= P(Z > -1.3)

= 1 - P(Z < -1.3)

= 1 - 0.0968

= 0.9032

b) P(X > 3)

= P((X - )/ > (3 - )/)

= P(Z > (3 - 2.3)/1)

= P(Z > 0.7)

= 1 - P(Z < 0.7)

= 1 - 0.7580

= 0.2420

C) P(> 4.1)

= P(( - )/() > (4.1 - )/())

= P(Z > (4.1 - 2.3)/(1/) )

= P(Z > 5.4)

= 1 - P(Z < 5.4)

= 1 - 1 = 0