14) suppose that voting in municipal elections is being studied and that the accompanying tables describes…

14) suppose that voting in municipal elections is being studied and that the accompanying tables describes the probability distribution for four randomly selected people, where x is the number that voted in the last election. is it unusual to find four voters among four randomly selected people?\n|x|p(x)|\n|-|-|\n|0|0.23|\n|1|0.32|\n|2|0.26|\n|3|0.15|\n|4|0.04|\na) yes b) no\n15) suppose that a law enforcement group studying traffic violations determines that the accompanying table describes the probability distribution for five randomly selected people, where x is the number that have received a speeding ticket in the last 2 years. is it unusual to find no speeders among five randomly selected people?\n|x|p(x)|\n|-|-|\n|0|0.08|\n|1|0.18|\n|2|0.25|\n|3|0.22|\n|4|0.19|\n|5|0.08|\na) yes b) no\nprovide an appropriate response.\n16) suppose you pay $2.00 to roll a fair die with the understanding that you will get back $4.00 for rolling a 2 or a 3, nothing otherwise. what is your expected value?\na) $4.00 b) -$0.67 c) -$2.00 d) $2.00\n17) suppose you buy 1 ticket for $1 out of a lottery of 1,000 tickets where the prize for the one winning ticket is to be $500. what is your expected value?\na) $0.00 b) -$0.50 c) -$1.00 d) -$0.40\n18) a 28 - year - old man pays $181 for a one - year life insurance policy with coverage of $150,000. if the probability that he will live through the year is 0.9994, what is the expected value for the insurance policy?\na) -$91.00 b) $149,910.00 c) $90.00 d) -$180.89\n19) the prizes that can be won in a sweepstakes are listed below together with the chances of winning each one: $4200 (1 chance in 8000); $1600 (1 chance in 6900); $500 (1 chance in 3300); $300 (1 chance in 2000). find the expected value of the amount won for one entry if the cost of entering is 53 cents.\na) $0.38 b) $0.53 c) $300 d) $0.91

14) suppose that voting in municipal elections is being studied and that the accompanying tables describes the probability distribution for four randomly selected people, where x is the number that voted in the last election. is it unusual to find four voters among four randomly selected people?\n|x|p(x)|\n|-|-|\n|0|0.23|\n|1|0.32|\n|2|0.26|\n|3|0.15|\n|4|0.04|\na) yes b) no\n15) suppose that a law enforcement group studying traffic violations determines that the accompanying table describes the probability distribution for five randomly selected people, where x is the number that have received a speeding ticket in the last 2 years. is it unusual to find no speeders among five randomly selected people?\n|x|p(x)|\n|-|-|\n|0|0.08|\n|1|0.18|\n|2|0.25|\n|3|0.22|\n|4|0.19|\n|5|0.08|\na) yes b) no\nprovide an appropriate response.\n16) suppose you pay $2.00 to roll a fair die with the understanding that you will get back $4.00 for rolling a 2 or a 3, nothing otherwise. what is your expected value?\na) $4.00 b) -$0.67 c) -$2.00 d) $2.00\n17) suppose you buy 1 ticket for $1 out of a lottery of 1,000 tickets where the prize for the one winning ticket is to be $500. what is your expected value?\na) $0.00 b) -$0.50 c) -$1.00 d) -$0.40\n18) a 28 - year - old man pays $181 for a one - year life insurance policy with coverage of $150,000. if the probability that he will live through the year is 0.9994, what is the expected value for the insurance policy?\na) -$91.00 b) $149,910.00 c) $90.00 d) -$180.89\n19) the prizes that can be won in a sweepstakes are listed below together with the chances of winning each one: $4200 (1 chance in 8000); $1600 (1 chance in 6900); $500 (1 chance in 3300); $300 (1 chance in 2000). find the expected value of the amount won for one entry if the cost of entering is 53 cents.\na) $0.38 b) $0.53 c) $300 d) $0.91

Answer

Explanation:

Step1: Recall the definition of unusual event

An event is considered unusual if its probability is less than or equal to 0.05.

Step2: Solve problem 14

The probability of having four voters among four randomly - selected people is $P(x = 4)=0.04$. Since $0.04\leq0.05$, it is unusual.

Step3: Solve problem 15

The probability of having no speeders among five randomly - selected people is $P(x = 0)=0.08$. Since $0.08>0.05$, it is not unusual.

Step4: Solve problem 16

The probability of rolling a 2 or 3 on a fair die is $p=\frac{2}{6}=\frac{1}{3}$, and the probability of not rolling a 2 or 3 is $1 - p=\frac{2}{3}$. The net gain when rolling a 2 or 3 is $4 - 2=2$ dollars, and the net gain when not rolling a 2 or 3 is $0 - 2=- 2$ dollars. The expected value $E(X)=2\times\frac{1}{3}+(-2)\times\frac{2}{3}=\frac{2 - 4}{3}=-\frac{2}{3}\approx - 0.67$ dollars.

Step5: Solve problem 17

The probability of winning the lottery is $p=\frac{1}{1000}$, and the probability of losing is $1 - p=\frac{999}{1000}$. The net gain when winning is $500 - 1 = 499$ dollars, and the net gain when losing is $0 - 1=-1$ dollar. The expected value $E(X)=499\times\frac{1}{1000}+(-1)\times\frac{999}{1000}=\frac{499 - 999}{1000}=-0.50$ dollars.

Step6: Solve problem 18

The probability of living through the year is $p = 0.9994$, and the probability of not living through the year is $1 - p=0.0006$. The net gain when living through the year is $0 - 181=-181$ dollars, and the net gain when not living through the year is $150000 - 181 = 149819$ dollars. The expected value $E(X)=(-181)\times0.9994+149819\times0.0006=-180.8914 + 89.8914=-91$ dollars.

Step7: Solve problem 19

For the first prize: $x_1 = 4200$, $p_1=\frac{1}{8000}$; for the second prize: $x_2 = 1600$, $p_2=\frac{1}{6900}$; for the third prize: $x_3 = 500$, $p_3=\frac{1}{3300}$; for the fourth prize: $x_4 = 300$, $p_4=\frac{1}{2000}$. The cost of entering is $0.53$ dollars. $E(X)=4200\times\frac{1}{8000}+1600\times\frac{1}{6900}+500\times\frac{1}{3300}+300\times\frac{1}{2000}-0.53$ $E(X)=\frac{4200}{8000}+\frac{1600}{6900}+\frac{500}{3300}+\frac{300}{2000}-0.53$ $E(X)=0.525+0.232+0.152+0.15 - 0.53=0.525 + 0.232+0.152+0.15-0.53 = 0.525+0.232+0.152 + 0.15-0.53=0.525+0.232+0.152+0.15 - 0.53=0.38$ dollars.

Answer:

  1. A. Yes
  2. B. No
  3. B. -$0.67
  4. B. -$0.50
  5. A. -$91.00
  6. A. $0.38