Part -1:
1. If the probability of success is 0.4 and the number of trials in a binomial distribution is 150, then its standard deviation is 36.
2. If a fair coin is tossed 20 times then the probability of exactly 10 Tails is more than 18 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.
Part -2:
4. For a continuous distribution, P(X ≤ 100) is larger than P(X < 100).
5. A continuous random variable may not be normally distributed.
6. The variance of the standard normal distribution is always 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.
Part -3:
8. The standard deviation of all possible sample proportions decreases as the sample size decreases.
9. If the population is normally distributed then the sample must be normally distributed even for small sample size.
Part -4:
10. 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.
11. When the population is normally distributed and the population standard deviation σ is unknown, then for any sample size n, the sampling distribution of x' is based on the t distribution.
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.
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 small than when s is large.
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.
15. The sample mean, the sample proportion and the sample standard deviation are all unbiased estimators of the corresponding population parameters.