Prompt Which provides a better estimate of the theoretical probability P(H) for the unfair coin: an empirical probability using 30 flips or 1000 flips? Why do you think so?

Here is a list of the problems. Answers need to be provided in the attached Word document. 1.The singular form of the word “dice” is “die”. Tom was throwing a six-sided die. The first time he threw, he got a three; the second time he threw, he got a three again. What’s the probability of getting a three at the third time? 2.There are 30 table tennis balls in the box: 6 are green, 10 are red, and 14 are yellow. If you shake the box and then randomly select one ball from the box, what’s the probability that you will get a red one: 3. Rachel was flipping a coin with Jerry. She told jerry: “I am able to get all heads in two tosses.” Jerry laughed at her: “No, the probability of getting two heads at two tosses is only__” 4. Jennie and Alex both wanted to get a free ticket for a College Music concert. However, the concert staff told them the tickets were limited. Twenty people wanted to attend the concert but only 10 free tickets were left. So the concert center staff decided to use a lottery to decide who would receive the free tickets. What’s the probability of Jennie and Alex both getting free tickets? 5.Laura and Melissa were playing dice. What the probability of Laura and Melissa both getting a 6? 6. In a statistics class with 36 students, the professor wanted to know the probability that at least two students share the same birthday. The probability will be___ a. 0.1 b. Much smaller than 0.1 c. Much bigger than 0.1 d. Not possible 7. If you throw a die for two times, what is the probability that you will get a one on the first throw or a one on the second throw (or both)? 8. Jerry got a box full of colorful candy balls. There were 50 of them: 20 red, 10 green, 12 yellow and 8 blue. After shaking the box, he randomly selected 2 candy balls from the box. What’s the probability that the first one was blue and the second one was yellow? 9.Jerry got a box full of colorful candy balls. There were 50 of them: 20 red, 10 green, 12 yellow and 8 blue. After shaking the box, he randomly selected 2 candy balls from the box. What’s the probability that the first is blue and the second one is also blue? 10. Which activity could probabilities be computed using a Binomial Distribution? a. Flipping a coin a 100 times b. Throwing a die one hundred times c. The probability of getting a heart while playing card games d. Grades earned by 100 students on a statistics final exam 11. Many researchers have argued that the TB skin test is not accurate. Imagine that the TB skin test is only 70% accurate. Sarah is thinking about having the test. Before she has the test she wonders the probability that she has TB. The probability of Sarah having TB is … a. 70% b. 35% c. 30% d. More information needed to calculate 12. Imagine that the diabetic test accurately indicates the disease in 95% of the people who have it. What’s the miss rate? 13. Which of the following is the probability that subjects do not have the disease, but the test result is positive? a. Miss rate b. False positive rate c. Base rate d. Disease rate 14. In a normal distribution, the median is ____it’s mean and mode. a. Approximately equal to b. Bigger than c. Smaller than d. Unrelated to 15. In a normal distribution, __ percentage of the area under the curve is within one standard deviations of the mean? a. 68% b. 100% c. 95% d. It depends on the values of the mean and standard deviation 16. A normal distribution with a mean of 15 and standard deviation of 5. 95% of its area is within__ a. One standard deviation of the mean b. Two standard deviations of the mean c. Three standard deviations of the mean d. It depends on the value of the mode 17.The mean of a standard normal distribution is: a. 0 b. 1.0 c. -1.0 d. 100 18. The standard deviation of the mean for a standard distribution is: a. 0.0 b. 1.0 c. 100 d. 68% 19. A normal distribution with a mean of 25 and standard deviation of 5. What is the corresponding Z score for a case having a value of 10? 20. Consider a normal distribution with a mean of 25 and standard deviation of 4. Approximately, what proportion of the area lies between values of 17 and 33. a. 95% b. 68% c. 99% d. 50% 21. Consider a normal distribution with a mean of 10 and standard deviation of 25. What’s the Z score for the value of 35? 22. For a standard normal distribution, what’s the probability of getting a positive number? a. 50% b. 95% c. 68% d. We cannot tell from the given information 23.Two-hundred students took a statistics class. Their professor creatively decided to give each of them their Z-score instead of their grade. Rachel got her Z-score of -0.2. She was wondering how well she did on the exam. a. It was very good, much better than almost all of the other students b. It was so-so, but still better than half of the students. c. It was not that good, but not at the bottom of the distribution d. It was very bad and she needs to work much harder next time 24. A researcher collected some data and they form a normal distribution with a mean of zero. What’s the probability of getting a positive number from this distribution? a. 25% b. 50% c. 75% d. We need to calculate the standard deviation and then decide. 25. Which of the following description of distribution is correct? a. A Binomial distribution is a probability distribution for independent events for which there are only two possible outcomes b. You cannot use the normal distribution to approximate the binomial distribution c. Normal distributions cannot differ in their means and in their standard deviations. d. Standard normal distributions can differ in their means and in their standard deviations. 26. A toy factory makes 5,000 teddy bears per day. The supervisor randomly selects 10 teddy bears from all 5,000 teddy bears and uses this sample to estimate the mean weight of teddy bears and the sample standard deviation. How many degrees of freedom are there in the estimate of the standard deviation? 27. Imagine you have a population of 100,000 cases. For which of the following degrees of freedom is the closest estimation of the population parameter? a. 4 b. 6 c. 10 d. 1000 28.Imagine that the average weight of a total of 500 girls in a high school is 35kg. Tom randomly sampled 10 girls and measured their weight. And then he repeated this procedure for three times. The means and standard deviations are listed as following. Which sample estimate shows the least sample variability? a. Sample one: mean=34, SE=5 b. Sample two: mean=30, SE=2 c. Sample three: mean= 26, SE=3 d. Sample four: mean= 38, SE=5 29. For which of the following degrees of freedom is a t distribution closest to a normal distribution? a. 10 b. 20 c. 5 d. 1000 30. In order to construct a confidence interval for the difference between two means, we are going to assume which of the followings? (Select all that apply) a. The two populations have the same variance. b. The populations are normally distributed. c. Each value is sampled independently from each other value. d. The two populations have similar means 31. A researcher tries to compare grades earned on the first quiz by boys and girls. He randomly chooses 10 students from boys and 15 students from girls and calculates the confidence interval on difference between means. How many degrees of freedom will you get in this t distribution? 32. Which of the following choices is not the possible confidence interval on the population values of a Pearson’s correlation? a. (0.3, 0.5) b. (-0.7, 0.9) c. (-1.2, 0.3) d. (0.6, 0.8)33. Which of the following descriptions of the t distribution is correct? (Select all that apply) a. With smaller sample sizes, the t distribution is leptokurtic b. When the sample size is large (more than 100), the t distribution is very similar to the standard normal distribution c. With larger sample sizes, the t distribution is leptokurtic d. The t distribution will never be close to normal distribution 34. _________________refers to whether or not an estimator tends to overestimate or underestimate a parameter. ______________ is the standard deviation of the sampling distribution and play a critical role in the constructing confidence intervals and in significance testing.a. Bias; standard error b. Sample population; Bias c. Mean; standard deviation d. Standard deviation; Mean 35. Which of the following descriptions of confidence intervals is correct? a. Confidence intervals can only be computed for the mean b. We can only use the normal distribution to compute confidence intervals c. Confidence intervals can be computed for various parameters d. Confidence intervals can only be computed for the population