1. The mean incubation time of fertilized chicken eggs keep at 100.5oF in a still-air incubator is 21 days. Suppose that the incubation times are approximately normally distributed with standard deviation of 1 day. If you are taking 400 random sample eggs and record the incubation time. a. What is standard deviation for the average time? b. Use the 99.7% of the data, describe the variability of this sample mean c. What is the probability that a randomly selected fertilized chicken egg hatches in less than 20 days? d. If you increase the sample size by n x 16, how this will affect standard deviation of the sample mean? 2. A Gallup Poll finds that 22% of Maryland residents visited Casino in the past 12 months. You decide to interview a random sample of 20 residents from Washington, D.C. if they visited Casino in the last 12 months. (Assume that this survey follows a Binomial Distribution). a. What is the mean and distribution (of the sample mean of DC residents visiting Casino in the past 12 months? b. If you increase the sample size by n x 16, how this will affect standard deviation of the sample mean? c. What is the probability that at least 18 of them visited the Casino in the last 12 months? 3. According to the American Lung Association, 90% of adult smokers started smoking before turning 21 years old. Ten smokers 21 years old or older are randomly selected and the number of smokers who started smoking before 21 is recorded. a. What is the mean and distribution the binomial distribution? b. What is the probability that exactly 6 of them started smoking before turning 21 years? c. What is the probability that at least 7 of them started smoking before 21 years of age? d. What is the probability that 4 to 6 of them started smoking before turning 21 years? 4. According to the credit reporting Transunion, the mean credit card debt in the United States among individuals with credit cards for the period between April and June of 2014 was $5241. Treating the results of the StatCrunch survey as a random sample of U.S. residents, determine whether there is evidence to suggest that credit card debt is lower than $5241. Use the 0.05 level of significance