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1. When you toss a fair six-faced die two times many outcomes can happen: a

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1. When you toss a fair six-faced die two times many outcomes can happen:
a) Determine the number of possible outcomes in the sample space. Explain your answer.

b) Calculate the probability that you get a number greater than 5 at the first toss. Show work and write the answer in the simplest fraction form.

c) Calculate the probability that the sum of the two tosses is at lest 7. Show work and write the answer in the simplest fraction form.

d) Calculate the probability that the sum of the two tosses is at least 7, given that you get a number greater than 2 in the first toss. Show work and write the answer in the simplest fraction form.

e) If event A is “Getting a number greater than 4 in the first toss”, and event B is “The sum of two tosses is at least 8”. Are event A and event B independent. Justify your answer.

4. The SAT Math scores for all seniors in a High Schools are normally distributed with population standard deviation of 200. If 100 seniors from the school are randomly selected, and their SAT Math scores have a sample mean of 650, determine:

a) What distribution will you use to determine the critical value for a confidence interval estimate of the mean SAT Math score for the seniors in the High School? Why?

b) Construct a 95% confidence interval estimate of the mean Math score for the seniors in the High School. Show work and round the answer to two decimal places.

 
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