## (solution) 3 questions is statistic . due in 45 mins........................

3 questions is statistic . due in 45 mins........................

Weary of the low turnout in student elections, a college administration decides to choose an SRS

of three students to form an advisory board that represents student opinion. Suppose that 36% of

all students oppose the use of student fees to fund student interest groups, and that the opinions

of the three students on the board are independent. Then the probability is 0.36 that each opposes

the funding of interest groups.

(a) Call the three students A, B, and C. Give the probability of each possible outcomes (Ac, Bc, Cc

are the events that the students support the student fee usage).

Pr(ABC) =

0.0466 Pr(ABCc) =

0.262144 Pr(ABcC) =

0.1474 Pr(AcBC) =

Pr(ABcCc) =

Pr(AcBCc) =

Pr(AcBcC) =

Pr(AcBcCc) = (b) Let the random variable X be the number of student representatives who oppose the funding

of interest groups. Give the probability distribution of X.

X

0

1

2

3

P(X)

(c) Find P (a majority of the advisory board opposes funding). Let the random variable X be a random number with the uniform density curve in the figure

below. Find the following probabilities:

(a)

P(X ? 0.25) (b)

P(X = 0.25) (c)

P(0.25 &lt; X &lt; 1.45) (d)

P(0.10 ? X ? 0.20 or 0.6 ? X ? 0.8) 0.3 (e) The probability that X is not in the interval 0.5 to 0.7.

0.2 7. 1/5 points | Previous Answers MIntroStat6 4.E.063.

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Question Part

Many random number generators allow users to specify the range of the random numbers to be

produced. Suppose that you specify that the range is to be all numbers between 0 and 4. Call the

random number generated Y. Then the density curve of the random variable Y has constant height

between 0 and 4, and height 0 elsewhere.

(a) What is the height of the density curve between 0 and 4? (Enter your answer to two decimal

places.)

0.25 Draw a graph of the density curve. (b) Use your graph from (a) and the fact that probability is area under the curve to find

P(Y ? 1.9).

(Enter your answer to three decimal places.)

0 (c) Find

P(0.2 &lt; Y &lt; 1.8).

(Enter your answer to three decimal places.) (d) Find

P(Y ? 0.7).

(Enter your answer to three decimal places.)

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