# Assignment 2

**Topics:**Normal distribution, Standard deviation, Probability theory

**Pages:**5 (3222 words)

**Published:**October 28, 2014

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 normally distributed then the sample mean may or may not be normally distributed for small sample size. FALSE If the population is normally distributed then the sample mean is also normally distributed even for small sample size.(Instructions on Ch 7, property 4)Chapter 810. First a confidence interval is constructed without using the finite population correction factor. Then, for the same identical data, a confidence interval is constructed using the finite population correction factor. The width of the interval without the finite population correction factor is wider than the confidence interval with the finite population correction factor. TRUE 11. When the population is normally distributed and the population standard deviation is unknown, then for any sample size n, the sampling distribution of X is based on the t distribution. TRUE 12. When the level of confidence and sample standard deviation remain the same, a confidence interval for a population mean based on a sample of n=100 will be narrower than a confidence interval for a population mean based on a sample of n= 150. FALSE 13. When the level of confidence and the sample size remain the same, a confidence interval for a population mean µ will be narrower, when the sample standard deviation s is large than when s is small. False 14. When the level of confidence and sample proportion p remain the same, a confidence interval for a population proportion p based on a sample of n=100 will be wider than a confidence interval for p based on a sample of n=400. TRUE 15. The sample mean and the sample proportion are unbiased estimators of the corresponding population parameters. TRUE But the Sample Standard Deviation is not an unbiased estimator. Multiple Choice (2 points each)

Chapter 51. In a study conducted by UCLA, it was found that 25% of college freshmen support increased military spending. If 6 college freshmen are randomly selected, find the probability that at least 3 support increased military...

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