Question

Instructions: No electronics other than a calculator. Show your work for credit. All probability answers rounded to four decimal places, ten- thousandths.

1) In a classroom there are 4 physics majors, 6 chemistry majors, and 3 math majors. The professor chooses 5 at random from this group to form a team for an academic competition. What is the probability the team has 3 chemistry majors?
2) In a survey, 30% of the people interviewed said that they bought most of their books during the last three months of the year (October, November, and December). If nine people ae selected at random, what is the probability that exactly three of these people bought most of their books during October, November and December?
3) What is the mean and standard deviation for the numbers of heads when ten fair coins are tossed?

Answer 1

The probability that a physics major will do postgraduate research for four years is 0.25 or 25%. The probability that a physics major will do postgraduate research for at most three years is 0.9 or 90%. On average, a physics major would spend approximately 1.9 years doing postgraduate research.

Step-by-step explanation:

26. To find the probability that a physics major will do postgraduate research for four years, we look at the probability distribution given by the professor. In this case, we find that P(x=4) = 0.25. So, the probability is 0.25 or 25%.

27. To find the probability that a physics major will do postgraduate research for at most three years, we sum up the probabilities for x=0, x=1, x=2, and x=3. P(x ≤ 3) = P(x=0) + P(x=1) + P(x=2) + P(x=3) = 0.1 + 0.3 + 0.35 + 0.15 = 0.9. So, the probability is 0.9 or 90%.

28. To find the average number of years a physics major would spend doing postgraduate research, we multiply each possible outcome by its probability according to the distribution and sum them up. In this case, the calculation would be: E(x) = 0 * 0.1 + 1 * 0.3 + 2 * 0.35 + 3 * 0.15 + 4 * 0.1 = 1.9. So, on average, a physics major would spend approximately 1.9 years doing postgraduate research.