# Exam preparation with solution

**Topics:**Probability theory, Standard deviation, Arithmetic mean

**Pages:**2 (665 words)

**Published:**October 28, 2014

1.

The number of calls coming into a PBX has a mean of 120 calls per hour. What is the probability of no calls in a one-minute interval? .1353

2.

A school is sending 18 children to a camp. If 15% of the children in the school are first graders, and the 18 children are selected at random from among all 6 grades at the school, find the mean and variance of the number of first graders chosen? The mean is 2.7, and the variance is 2.3.

n = 18

p = .15

q = .85

Mean = np = 18 x .15 = 2.7

Variance = npq = (18 x .15 x .85) = 2.295 ≈ 2.3

3. A producer plans an outdoor regatta for May 3. The cost of the regatta is $8000, which includes advertising, security, printing tickets, entertainment, etc. The producer plans to make $15,000 profit if all goes as planned. However, if it rains, the regatta will have to be canceled. According to the weather report, the probability of rain is 0.3. Find the producer’s expected profit. $8100 μ = (15,000 X .70) + (-8,000 x .30) = $8,100

4. Historical data shows that the average number of patient arrivals at the intensive care unit of General Hospital is 3 patients every 2 hours. Determine the probability of at least 4 but no more than 8 patients arriving in a three-hour period. .6174

P(X = 4) .1898

P(X = 5) .1708

P(X = 6) .1281

P(X = 7) .0824

P(X = 8).0463

P (4 ≤ X ≤ 8) = (.0463) + (.0824) + (.1281) + (.1708) + (.1898) = .6174

5.

A student takes a 7 question multiple-choice quiz with 4 choices for each question. If the student guesses at random on each question, what is the probability that the student gets exactly 3 questions correct? 0.173

n = 7 p = .25 q = .75 P(X = 3)

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BUS216 Exam #2 Review – Discrete Distributions

= 0.172759 ≈ 0.173 or 17.3%

6. The R.U. Scared Company buys inflatable Halloween yard decorations from a Korean supplier. The probability of a defective decoration is 10%. If 100 decorations are selected at random, what...

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