Question

Last semester, the students in my Finite Math class had an average quiz score of 83 with a standard deviation of 2. Assume that the scores are approximated by a normal distribution. a) What percent of students scored higher than an 86 on the quiz? b) What percent of students scored less than a 79 on the quiz? c) What percent of students scored between a 79 and an 86? d) What happens when you try to find the percent of students that scored less than a 60?

Problem 3: You play a game where you spin a spinner with the numbers 1 through 10 on it in equal parts. It costs $7 to play. If you spin a two then you win $25. If you spin an odd number then you win $10. You decide to play the game once. What are your expected winings?

Answer 1

Last semester, the students in my Finite Math class had an average quiz score of 83 with a standard deviation of 2. Assume that the scores are approximated by a normal distribution. a) What percent of students scored higher than an 86 on the quiz? b) What percent of students scored less than a 79 on the quiz? c) What percent of students scored between a 79 and an 86? d) What happens when you try to find the percent of students that scored less than a 60?

It is given that

a) What percent of students scored higher than an 86 on the quiz? ie P(X>86)

We know that follows a standard normal distribution. When X=86,

  

  

b) What percent of students scored less than a 79 on the quiz? ie P(X<79)*100.

When X=79,

.

Therefore 2.28% percent of students scored less than a 79 on the quiz.

c) What percent of students scored between a 79 and an 86?

Since we calculated the probalities already we make use of Normal probbility

ie P(79<X<86)=1-P(X<79)-P(X>86)=1-0.0228-0.0668=1-0.0896=0.9104.

Therefore 91.04% of students sored between 79 and 86.

d) What happens when you try to find the percent of students that scored less than a 60?

P(X<60)

Here . This probability will almost be zero or negligible since we know that the probabilities are almost zero after 3 standard deviations.

Problem 3: You play a game where you spin a spinner with the numbers 1 through 10 on it in equal parts. It costs $7 to play. If you spin a two then you win $25. If you spin an odd number then you win $10. You decide to play the game once. What are your expected winings?

Here we are interested in only three outcomes ie spinning a two ,spinning an odd number and otherwise. It is given that the the outcomes are equal since it is divided in equal parts.

Therfore the probaility of getting a 2 ia 1/10, and getting an odd number is 5/10 and other numbers are 4/10.

The expected pay off distribution is therefore

  

Outcome	Payoff	probability	Exp
2	25	0.1	2.5
Odd#	10	0.5	5
Others	0	0.4	0
		Total	7.5

The expected gain is $7.5. Since it costed $7, the expected winnings=$7.5-$7.0=$0.5