91Ó°ÊÓ

According to a CBS/New York Times poll taken in \(1992,15 \%\) of the public have responded to a telephone call-in poll. In a random group of five people, what is the probability that exactly two have responded to a call-in poll? (A) \(10(0.15)^{2}(0.85)^{3}\) (B) \(5(0.15)^{2}(0.85)^{3}\) (C) \((0.15)^{2}(0.85)^{3}\) (D) \((0.15)^{2}\) (E) \(5(0.15)^{2}\)

An inspection procedure at a manufacturing plant involves picking three items at random and then accepting the whole lot if at least two of the three items are in perfect condition. If in reality \(90 \%\) of the whole lot are perfect, what is the probability that the lot will be accepted? (A) \(3(0.1)^{2}(0.9)\) (B) \(3(0.9)^{2}(0.1)\) (C) \((0.1)^{3}+(0.1)^{2}(0.9)\) (D) \((0.1)^{3}+3(0.1)^{2}(0.9)\) (E) \((0.9)^{3}+3(0.9)^{2}(0.1)\)

Sixty-five percent of all divorce cases cite incompatibility as the underlying reason. If four couples file for a divorce, what is the probability that exactly two will state incompatibility as the reason? (A) 2(0.65)(0.35) (B) \(2(0.65)^{2}(0.35)^{2}\) (C) \(4(0.65)^{2}(0.35)^{2}\) (D) \(6(0.65)^{2}(0.35)^{2}\) (E) 0.65

Suppose we have a random variable \(X\) where, for the values \(k\) \(=0, \ldots, 10,\) the associated probabilities are \(\left(\begin{array}{c}10 \\\ k\end{array}\right)(0.37)^{k}(0.63)^{10-k} .\) What is the mean of \(X ?\) (A) 0.37 (B) 0.63 (C) 3.7 (D) 6.3 (E) None of the above

Each hospital Internet security breach results in the theft of an average of 361 patient records with a standard deviation of 74 records. If there are 45 independent breaches during a one-year period, what is the expected value and standard deviation for the number of patient records stolen? (A) \(E\) (thefts) \(=\sqrt{45} \times 361 \quad\) SD (thefts) \(=\sqrt{45} \times 74\) (B) \(E(\) thefts \()=\sqrt{45} \times 361 \quad \mathrm{SD}(\) thefts \()=45 \times 74\) (C) \(E\) (thefts) \(=\sqrt{45} \times 361 \quad\) SD (thefts) \(=45 \times 74\) (D) \(\quad E(\) thefts \()=45 \times 361 \quad\) SD (thefts) \(=45 \times 74\) (E) \(E\) (thefts) \(=45 \times 361 \quad\) SD (thefts) \(=45 \times 74^{2}\)

It is estimated that two out of five high school students would fall victim to a phishing e-mail (an online scam asking for sensitive information) if it appears to originate from their high school main office. In a random sample of five high school students, what is the probability that exactly two fall victim to a phishing e-mail that appears to originate from their high school main office? (A) 0.4 (B) 1.0 (C) \(\left(\begin{array}{l}5 \\ 2\end{array}\right)(0.4)^{2}(0.6)^{3}\) (D) \(\left(\begin{array}{l}5 \\ 2\end{array}\right)(0.4)^{2}(0.6)^{3}\) (E) \((0.4)^{2}(0.6)^{3}\)

Suppose you toss a fair coin ten times and it comes up heads every time. Which of the following is a true statement? (A) By the law of large numbers, the next toss is more likely to be tails than another heads. (B) By the properties of conditional probability, the next toss is more likely to be heads given that ten tosses in a row have been heads. (C) Coins actually do have memories, and thus what comes up on the next toss is influenced by the past tosses. (D) The law of large numbers tells how many tosses will be necessary before the percentages of heads and tails are again in balance. (E) The probability that the next toss will again be heads is 0.5

It is estimated that two out of five high school students would fall victim to a phishing e-mail (an online scam asking for sensitive information) if it appears to originate from their high school main office. What is the probability that the first student to fall victim will be the third student who is sent a phishing e-mail that appears to originate from their high school main office? (A) \((0.4)^{3}\) (B) \((0.6)^{3}\) (C) (0.6)\((0.4)^{2}\) (D) \((0.6)^{2}(0.4)\) (E) \(\left(\begin{array}{l}5 \\ 2\end{array}\right)(0.6)^{2}(0.4)\)

Suppose a retailer knows that the mean number of broken eggs per carton is 0.3 with a standard deviation of 0.18 . In a shipment of 100 cartons, what is the expected number of broken eggs and what is the standard deviation? Assume independence between cartons. \(\begin{array}{ll}\text { (A) } E \text { (broken) }=3 & \text { SD(broken) }=1.8\end{array}\) (B) \(E(\) broken \()=30 \quad\) SD(broken) \(=1.8\) \(\begin{array}{ll}\text { (C) } E \text { (broken) }=30 & \text { SD(broken) }=18\end{array}\) (D) \(E\) (broken) \(=300 \quad\) SD(broken) \(=18\) (E) \(E(\) broken \()=300 \quad\) SD(broken \()=180\)

Boxes of 50 donut holes weigh an average of 16.0 ounces with a standard deviation of 0.245 ounces. If the empty boxes alone weigh an average of 1.0 ounce with a standard deviation of 0.2 ounces, what are the mean and standard deviation of donut hole weights? (A) \(E(\) Donut hole \()=0.3\) oz \(\quad \mathrm{SD}(\) Donut hole \()=0.0063 \mathrm{oz}\) (B) \(E(\) Donut hole \()=0.3\) oz \(\quad \mathrm{SD}(\) Donut hole \()=0.02 \mathrm{oz}\) (C) \(E(\) Donut hole \()=0.3\) oz \(\quad \mathrm{SD}(\) Donut hole \()=0.142 \mathrm{oz}\) (D) \(E(\) Donut hole \()=15\) oz \(\quad\) SD(Donut hole \()=0.142\) oz (E) \(E\) (Donut hole) \(=15\) oz \(\quad\) SD(Donut hole \()=0.445\) oz