Probability And Statistics | Week 5

Probability And Statistics Week 5 Answers

Link : Probability And Statistics (nptel.ac.in)

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

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

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

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

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

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

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 is 0.2033. Find the value of [k]?

(A) 10
(B) 11
(C) 12
(D) 13

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

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

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