1 answer

Please provide all answers according to question numbers thank you (2) A sample of students who...

Question:

Please provide all answers according to question numbers thank you
(2) A sample of students who have taken a calculus test has a mean score of 78.2, a mode of 67, and a median score of 67. Based on this information, what may one deduce about the distribution of the test scores? (a) It is symmetric. (b) It is right-skewed. (c) It is left-skewed. (d) It is bimodal. (3) What is the set of all simple events of an experiment called? (a) a population (b) a distribution (c) a sample space (d) a random sample 4) For two events A and B, suppose: A 0.3 0.4 Then P(AU B) is equal to? A0.1 0.2 (5) Suppose P(A)0.4, P(B) 0.3, and P(AnB)-0.12. Which one of the following statements correctly defines the relationship between events A and B (a) Events A and B are independent, but not mutually exclusive. (bEvents A and B are mutually exclusive, but not independent (c)Events A and B are neither mutually exclusive nor independent d) Events A and B are both mutually exclusive and independent (6) Suppose P(A)-0.80, P(B) 0.60 and P(AUB) 0.90. Then what is the value of P(AIB)? (7) From experience, a shipping company knows that the cost of delivering a small package within 24 hours is S14.80. The company charges S15.50 for shipment but guarantees to refund the charge if delivery is not made within 24 hours. If the company fails to deliver only 2% of its packages within the 24-hour period, what is the expected gain per package?
(8) Two hundred single-sport athletes were cross-classified according to gender, as shown in the table below. An athlete is selected at random. Gender Swimmer(S) Runner(R) Cyclist(C) Total 20 115 25 85 45 200 30 20 50 65 40 105 Female(F) Tot a) What is the probability that the athlete is a male? b) What is the probability that the athlete is female and a runner? c) What is the probability that the athlete is male given that the athlete is known to be a runner? d) What is the probability that the athlete is female or a swimmer or both? e) Are the events being a female and being a runner independent? Explain why or why not f) Are the events being a male and being a cyclist mutually exclusive? Explain why or why not. (9) You are a realtor considering listing a $500,000 house. The cost of advertising and providing food for other realtors during open showings is anticipated to cost you $5000. The house after four months, you lose the listing and receive nothing. You anticipate that the probability you sell your own listed house is 0.3, the probability that another agent sells your listing is 0.2, and the probability that the house is unsold after 4 months is 0.5. If you sell your own listed house, the commission is a hefty $30,000. If another realtor sells your listing, the commission is $15,000. The bottom lie You will not take the listing unless you anticipate earning at least $6000. Should you list the house? is quite unusual and you are given a four-month listing. If the house is unsold (10) The probability distribution of the number of accidents in North York, Ontario, each day is given by: x 0 2 35 0.20 0.15 0.25 0.15 0.20 0.05 Based on this distribution, what would be the expected number of accidents on a given day and what is the approximate value of the standard deviation of the number of accidents per day?
(2) A sample of students who have taken a calculus test has a mean score of 78.2, a mode of 67, and a median score of 67. Based on this information, what may one deduce about the distribution of the test scores? (a) It is symmetric. (b) It is right-skewed. (c) It is left-skewed. (d) It is bimodal. (3) What is the set of all simple events of an experiment called? (a) a population (b) a distribution (c) a sample space (d) a random sample 4) For two events A and B, suppose: A 0.3 0.4 Then P(AU B) is equal to? A0.1 0.2 (5) Suppose P(A)0.4, P(B) 0.3, and P(AnB)-0.12. Which one of the following statements correctly defines the relationship between events A and B (a) Events A and B are independent, but not mutually exclusive. (bEvents A and B are mutually exclusive, but not independent (c)Events A and B are neither mutually exclusive nor independent d) Events A and B are both mutually exclusive and independent (6) Suppose P(A)-0.80, P(B) 0.60 and P(AUB) 0.90. Then what is the value of P(AIB)? (7) From experience, a shipping company knows that the cost of delivering a small package within 24 hours is S14.80. The company charges S15.50 for shipment but guarantees to refund the charge if delivery is not made within 24 hours. If the company fails to deliver only 2% of its packages within the 24-hour period, what is the expected gain per package?
(8) Two hundred single-sport athletes were cross-classified according to gender, as shown in the table below. An athlete is selected at random. Gender Swimmer(S) Runner(R) Cyclist(C) Total 20 115 25 85 45 200 30 20 50 65 40 105 Female(F) Tot a) What is the probability that the athlete is a male? b) What is the probability that the athlete is female and a runner? c) What is the probability that the athlete is male given that the athlete is known to be a runner? d) What is the probability that the athlete is female or a swimmer or both? e) Are the events being a female and being a runner independent? Explain why or why not f) Are the events being a male and being a cyclist mutually exclusive? Explain why or why not. (9) You are a realtor considering listing a $500,000 house. The cost of advertising and providing food for other realtors during open showings is anticipated to cost you $5000. The house after four months, you lose the listing and receive nothing. You anticipate that the probability you sell your own listed house is 0.3, the probability that another agent sells your listing is 0.2, and the probability that the house is unsold after 4 months is 0.5. If you sell your own listed house, the commission is a hefty $30,000. If another realtor sells your listing, the commission is $15,000. The bottom lie You will not take the listing unless you anticipate earning at least $6000. Should you list the house? is quite unusual and you are given a four-month listing. If the house is unsold (10) The probability distribution of the number of accidents in North York, Ontario, each day is given by: x 0 2 35 0.20 0.15 0.25 0.15 0.20 0.05 Based on this distribution, what would be the expected number of accidents on a given day and what is the approximate value of the standard deviation of the number of accidents per day?

Answers

Solution:-

P(x) (x - u)2 9245 X*P(x) x u)2 20 0.25 20 4.6225 198 108 0.406125 0.5 0.0225 0.0056249999 225 4225 8.1225 18.235 684 0.05 0.25 Sum

10) The expected number of accidents on a given day is 2.15 and the approximate value of the standard deviation of the number of accidents per day is 1.5256.

E(z) = 〉 x * P(z)

E(x) = 2.15

P(z) * (1-μ

σ = V2.3275

σ 1.5256

.

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