Assignment 2
Assignments2 solutions: Due by Midnight Monday October 13th, 2014(drop box of week 2) (Chapters 5, 6, 7 and 8) Total 75 points.
True/False (1 point each)
Chapter 51. If the probability of success is 0.4 and the number of trials in a binomial distribution is 150, then its variance is 6. FALSE σ2= (np(1-p)) =(150*0.4*0.6) = 36. But the standard deviation is 6.
2. If a fair coin is tossed 20 times then the probability of less than 10 Tails is less than 0.4 (less than 40% chance). FALSE It is 41.19 percent
3. The probability that a person catches a cold during the cold and flu season is 0.3. If 10 people are chosen at random, the standard deviation for the number of persons catching cold is 1.45. (Hint: convert the problem to a binomial distribution problem). TRUE Here p = 0.3 and n=10. Therefore, variance = 10*0.3*0.7 = 2.1 and the standard deviation is sq. root of 2.1 = 1.45
Chapter 64. For any distribution, P(X ≤ 10) is greater than or equal to P(X < 10). False This can be true only for a discrete distribution. For a continuous distribution, the two probabilities are equal.5. All continuous random variables are normally distributed. FALSE Continuous random variables can be highly skewed and non-normal. Even if it is symmetrical it may not be normal but other distribution like t-distribution. A normal random variable is a popular example of a continuous random variable, but a continuous r.v. need not be normal.
6. The standard deviation of a standard normal distribution is always equal to 1. True. Its mean is zero and variance (or std deviation) equal to 1.7. If the sample size is as large as 1000, we can safely use the normal approximation to binomial even for small p. FALSE (Instructions on Ch6) : For example if p is .001 then np would be only 1 even if sample size is 1000.
Chapter 78. The standard deviation of the sampling distribution of sample proportions increases as the sample size increases. FALSE
9. If the population is
True/False (1 point each)
Chapter 51. If the probability of success is 0.4 and the number of trials in a binomial distribution is 150, then its variance is 6. FALSE σ2= (np(1-p)) =(150*0.4*0.6) = 36. But the standard deviation is 6.
2. If a fair coin is tossed 20 times then the probability of less than 10 Tails is less than 0.4 (less than 40% chance). FALSE It is 41.19 percent
3. The probability that a person catches a cold during the cold and flu season is 0.3. If 10 people are chosen at random, the standard deviation for the number of persons catching cold is 1.45. (Hint: convert the problem to a binomial distribution problem). TRUE Here p = 0.3 and n=10. Therefore, variance = 10*0.3*0.7 = 2.1 and the standard deviation is sq. root of 2.1 = 1.45
Chapter 64. For any distribution, P(X ≤ 10) is greater than or equal to P(X < 10). False This can be true only for a discrete distribution. For a continuous distribution, the two probabilities are equal.5. All continuous random variables are normally distributed. FALSE Continuous random variables can be highly skewed and non-normal. Even if it is symmetrical it may not be normal but other distribution like t-distribution. A normal random variable is a popular example of a continuous random variable, but a continuous r.v. need not be normal.
6. The standard deviation of a standard normal distribution is always equal to 1. True. Its mean is zero and variance (or std deviation) equal to 1.7. If the sample size is as large as 1000, we can safely use the normal approximation to binomial even for small p. FALSE (Instructions on Ch6) : For example if p is .001 then np would be only 1 even if sample size is 1000.
Chapter 78. The standard deviation of the sampling distribution of sample proportions increases as the sample size increases. FALSE
9. If the population is