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1. For each of the following determine if it is a valid probability distribution. Show your work. If it is a probability distribution, find the expected value. a) k P(X=k) 0 1/2 1 ¼ b) P(X) 3 ½ 5 2 ½ 7 3 18 9 5/24 2. A company produces plastic parts with a defect rate of 5%. A sample of 20 parts is examined. Find the probability that at least two are defective. 3. The probability that a 17-or-18-year-old driver will have at least one accident in any year is 0.04. An insurance company has 348 17-or-18 year old drivers insured. a) Find the expected number of accidents among the 348 drivers. b) Find the probability that exactly 14 of them will have at least one accident.

1. For each of the following determine if it is a valid probability distribution. Show your work. If it is a probability distribution, find the expected value. a) k P(X=k) 0 1/2 1 ¼ b) P(X) 3 ½ 5 2 ½ 7 3 18 9 5/24 2. A company produces plastic parts with a defect rate of 5%. A sample of 20 parts is examined. Find the probability that at least two are defective. 3. The probability that a 17-or-18-year-old driver will have at least one accident in any year is 0.04. An insurance company has 348 17-or-18 year old drivers insured. a) Find the expected number of accidents among the 348 drivers. b) Find the probability that exactly 14 of them will have at least one accident.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. For each of the following determine if it is a valid probability distribution. Show your work. If it is a probability distribution, find the expected value. a) k P(X=k) 0 1/2 1 ¼ b) P(X) 3 ½ 5 2 ½ 7 3 18 9 5/24 2. A company produces plastic parts with a defect rate of 5%. A sample of 20 parts is examined. Find the probability that at least two are defective. 3. The probability that a 17-or-18-year-old driver will have at least one accident in any year is 0.04. An insurance company has 348 17-or-18 year old drivers insured. a) Find the expected number of accidents among the 348 drivers. b) Find the probability that exactly 14 of them will have at least one accident.
Transcribed Image Text:1. For each of the following determine if it is a valid probability distribution. Show your work. If it is a probability distribution, find the expected value. a) k P(X=k) 0 1/2 1 ¼ b) P(X) 3 ½ 5 2 ½ 7 3 18 9 5/24 2. A company produces plastic parts with a defect rate of 5%. A sample of 20 parts is examined. Find the probability that at least two are defective. 3. The probability that a 17-or-18-year-old driver will have at least one accident in any year is 0.04. An insurance company has 348 17-or-18 year old drivers insured. a) Find the expected number of accidents among the 348 drivers. b) Find the probability that exactly 14 of them will have at least one accident.
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