# Probability And Statistics | Week 5

**Course Name: Probability And Statistics**

**Course Link: Click Here**

**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

**Answer: (C) -1/ √2π**

**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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**These are Probability And Statistics Week 5 Assignment 5 Answers**