These are Probability And Statistics Week 5 Assignment 5 Answers
Q1. A linkage component X ~ N(12,0.01). LetY = 20X + 3. Find P(239 <= Y <= 241). (A) 0.1359 (B) 0.4962 (C) 0.2032 (D) 0.7081
Answer: (A) 0.1359
Q2. It is noted that 5% of pages on a corporate website contain errors. If 100 pages are checked randomly. find the probability that at least one of the checked pages has errors. (A) 0.8856 (B) 0.9941 (C) 0.0052 (D) 0.0214
Answer: (B) 0.9941
These are Probability And Statistics Week 5 Assignment 5 Answers
Q3. Suppose X be a standard normal random variable. Find P(X < 0| |[X]| = 1). (A) Φ(1)-0.5/Φ(2)-0.5 (B) Φ(1)+0.5/Φ(2)-0.5 (C) Φ(1)-0.5/Φ(2)+0.5 (D) Φ(1)+0.5/Φ(2)+0.5
Answer: (A) Φ(1)-0.5/Φ(2)-0.5
Q4. The study region in central Phoenix. Arizona recorded 10500 asthma incidents in children in a 21-month period. Assuming that the number of asthma incidents follows a Poisson distribution. find P(X = 550), where X is the number of asthma incidents in a month. Use normal approximation to Poisson distribution. (A) 0.01196 (B) 0.99845 (C) 0.98804 (D) 0.95456
Answer: (A) 0.01196
These are Probability And Statistics Week 5 Assignment 5 Answers
Q5. The time until recharge for a battery in a laptop computer under common conditions is normally distributed with a mean of 260 minutes and a standard deviation of 50 minutes. What is the first quartile of battery life? (A) 225.4125 (B) 226.1935 (C) 226.2755 (D) 220.3156
Answer: (C) 226.2755
Q6. Suppose Z be a standard normal distribution. Find E[min {Z, 0}]. (A) √1/π (B) 1- √2/π (C) -1/√2π (D) 1-1/π
These are Probability And Statistics Week 5 Assignment 5 Answers
Q7. The IQ level of a group of students is assumed to be normally distributed with mean 110 and standard deviation 15. The probability that a randomly selected student has an IQ of at least 110 + k 1s 0.2033. Find the value of [k]? (A) 10 (B) 11 (C) 12 (D) 13
Answer: (C) 12
Q8. The diameter of a dot produced by a printer is normally distributed with a mean diameter of 0.005cm and standard deviation of 0.001cm. What is the probability that a diameter is between 0.0035 and 0.0065cm? (A) 07529 (B) 0.8664 (C) 05269 (D) 0.2145
Answer: (B) 0.8664
These are Probability And Statistics Week 5 Assignment 5 Answers
Q9. The lifetime (in months) of a semiconductor laser follows log-normal distribution with mean 10 and standard deviation 1.5. What is the probability that lifetime exceeds 15 months? (A) 0.2156 (B) 0.4652 (C) 0.002613 (D) 0.6429
Answer: (C) 0.002613
Q10. Assume that the life (in years) of a packaged magnetic disc exposed to corrosive gases has a Weibull distribution with @ = 1 and B = k. What is the value of k so that the probability that the disc fails before 2 years is 0.708? A) 0.1 (B) 0.4 (C) 0.2 (D) 0.3
Answer: (D) 0.3
These are Probability And Statistics Week 5 Assignment 5 Answers
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