You flip a coin FOUR times. Let H = Number of Heads. Calculate: 1. P (H = 4) = 2. P (H 1) = 3. P (H < 4) = 4. P (1 < H 4) = HINT: GET YOUR SAMPLE SPACE. Leave your answers EITHER as a simplified fraction ( e.g. 4/16 = 1/4 when simplified) OR a decimal rounded to FOUR decimal places. Also do not forget to enter your leading zero when entering decimals. As reported by the Federal Bureau of Investigation in Crime in the United States, the age distribution of murder victims between 20 and 59 years old is as shown in the following table. Q21 A murder case in which the person murdered was between 20 and 59 years old is selected at random. Find the probability that the murder victim was: 1. Between 40 and 44 years old, inclusive. 2. At least 25 years old. 3. Between 45 and 59 years old, inclusive. 4. Under 30 or over 54. Leave your answers EITHER as a simplified fraction ( e.g. 4/16 = 1/4 when simplified) OR a decimal rounded to FOUR decimal places. Also do not forget to enter your leading zero when entering decimals. A number of students were asked if they have taken Acting (A), Biology (B) or Chemistry (C). Study the Venn diagram below and use it to answer the following questions. Q22 1. How many students were surveyed? Students For the following questions, Leave your answers EITHER as an un-simplified fraction ( e.g. 4/16 is un-simplified) OR simplified fraction ( e.g. 4/16 = 1/4 when simplified) OR a decimal rounded to FOUR decimal places. Also do not forget to enter your leading zero when entering decimals. CAUTION: FOLLOW ROUNDING RULES CAREFULLY. YOU WILL NOT EARN CREDIT FOR ANSWERS ROUNDED INCORRECTLY. 2. P (A) = 3. P (B) = 4. P (C) = 5. P (Acting only) = 6. P (Biology only) = 7. P (Chemistry only) = 8. P (Acting and Biology only) = 9. P (Acting and Chemistry only) = 10. P (Chemistry and Biology only) = 11. P (Acting and Biology and Chemistry) = 12. P (Acting or Biology) = 13. P (Acting or Chemistry) = 14. P (Chemistry or Biology) = 15. P (Acting or Biology or Chemistry) = 16. P (Neither Acting nor Biology nor Chemistry) = 17. P(Exactly two subjects) = 18. P(At least two subjects) = The U.S. Department of Agriculture publishes information about U.S. farms in Census of Agriculture. A joint frequency distribution for number of farms, by acreage and tenure of operator, is provided in the following contingency table. Frequencies are in thousands. Q23 1. How many full-owners own under 50 acres? (Enter a whole number only) 2. How many part-owners own 180 to under 500 acres? (Enter a whole number only) 3. How many tenants own 180 to under 500 acres? (Enter a whole number only) 4. How many farms are under 50 acres in size? (Enter a whole number only) 5. How many farm operators are tenants? (Enter a whole number only) 6. How many farms are represented in the table? (Enter a whole number only) A farm is randomly selected. Calculate the following probabilities. Leave your answers EITHER as a simplified fraction ( e.g. 4/16 = 1/4 when simplified) OR a decimal rounded to FOUR decimal places. Also do not forget to enter your leading zero when entering decimals. CAUTION: FOLLOW ROUNDING RULES CAREFULLY. YOU WILL NOT EARN CREDIT FOR ANSWERS ROUNDED INCORRECTLY. 7. The farm has either full owner or part owner tenure 8. The farm has tenant tenure or is 1000 & over Acres 9. The farm is T2 or A3 10. The farm is A2 or A4 The random variable X is the number of girls of four children born to a couple that is equally likely to have either a boy or a girl. Its probability distribution is as follows x 0 1 2 3 4 P(X = x) 0.0625 0.2500 0.3750 0.2500 0.0625 1. = E(X) = (Round your answer to one decimal place) 2. (X) = (Round your answer to one decimal place) 3. Among all families with four children, what is the average number of boys? (Round your answer to one decimal place) The first year the state of Pennsylvania issued railroad memorial license plates, the plates had a picture of a steam engine followed by four digits. Assuming that repetitions are allowed, how many railroad memorial plates could be issued? Answer-railroad memorial plates could be issued. In a club there are 7 women and 5 men. A committee of 3 women and 2 men is to be chosen. How many different possibilities are there? Answer- possibilities It is reported that 77% of workers aged 16 and over drive to work alone. Choose 8 workers at random. Let X represent the number of workers who drive alone. n = p = q = 1 - p = Find the probability that All drive to work alone More than one-half drive to work alone Exactly 3 drive to work alone = E(X) = (X) = (Round ALL answers to 4 decimal places. X.XXXX, 0.XXXX, .XXXX, X.X000 etc.,) A sales firm receives, on average, 3 calls per hour on its toll-free number. Let X represent the number of calls received in a given hour. Assuming X has a Poisson distribution. a) For any given hour, find the probability that it will receive the following. At most 3 calls At least 3 calls 5 or more calls b) Calculate = E(X) = (X) = (Round ALL answers to 4 decimal places. X.XXXX, 0.XXXX, .XXXX, X.X000 etc.,)