# Continuous Probability Distributions and Sampling Distributions

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1. Consider a multiple choice examination with 50 questions. Each question has four possible answers. Assume that a student who has done the homework and attended lectures has a 75% probability of answering any question correctly.

a) A student must answer 43 or more questions correctly to obtain a grade A. What percentage of the students who have done their homework and attended lectures will obtain a grade of A on this multiple choice examination?

b) A student who answers 35 to 39 questions correctly will receive a grade of C. What percentage of students who have done their homework and attended lectures will obtain a grade of C on this multiple choice examination?

c) A student must answer 30 or more questions correctly to pass the examination. What percentage of the students who have done their homework and attended lectures will pass the examination?

d) Assume that a student has not attended class and has not done the homework for the course. Furthermore, assume that the student will simply guess at the answer to each question. What is the probability that this student will answer 30 or more questions correctly and pass the examination?

2. The food marketing institute shows that 17% of households spend more than $100 per wee on groceries. Assume the population proportion is p=.17 and a simple random sample of 800 households will be selected from the population.

a) Show the sampling distribution of p, the sample proportion of households spending more than $100 per week on groceries.

b) What is the probability that the sample proportion will be with in plus or minus .02 of the population proportion?

c) Answer part (b) for a sample of 1600.

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