(a) If the variance of a data set is zero, then all the observations in this data set are zero.(b) If P(A) = 0.4 , P(B) = 0.5, and A and B are disjoint, then P(A AND B) = 0.9.(c) Assume X follows a continuous distribution which is symmetric about 0. If , then .(d) A 95% confidence interval is wider than a 90% confidence interval of the same parameter.(e) In a right-tailed test, the value of the test statistic is 1.5. If we know the test statistic follows a Students t-distribution with P(T < 1.5) = 0.96, then we fail to reject the null hypothesis at 0.05 level of significance .Refer to the following frequency distribution for Questions 2, 3, 4, and 5. The frequency distribution below shows the distribution for checkout time (in minutes) in UMUC MiniMart between 3:00 and 4:00 PM on a Friday afternoon.Checkout Time (in minutes)FrequencyRelative Frequency1.0 1.932.0 2.9123.0 3.90.204.0 4.935.0 -5.9Total25Complete the frequency table with frequency and relative frequency. Express the relative frequency to two decimal places. (5 pts)What percentage of the checkout times was at least 3 minutes? (3 pts)In what class interval must the median lie? Explain your answer. (5 pts)Does this distribution have positive skew or negative skew? Why? (2 pts)Refer to the following information for Questions 6 and 7. Consider selecting one card at a time from a 52-card deck. (Note: There are 4 aces in a deck of cards)If the card selection is without replacement, what is the probability that the first card is an ace and the second card is also an ace? (Express the answer in simplest fraction form) (5 pts)STAT 200: Introduction to Statistics Final Examination, Fall 2015 OL1/US1 Page 3 of 6If the card selection is with replacement, what is the probability that the first card is an ace and the second card is also an ace? (Express the answer in simplest fraction form) (5 pts)Refer to the following situation for Questions 8, 9, and 10.The five-number summary below shows the grade distribution of two STAT 200 quizzes for a sample of 500 students.MinimumQ1MedianQ3MaximumQuiz 115455585100Quiz 220355090100(4 pts each)Which quiz has less interquartile range in grade distribution?Which quiz has the greater percentage of students with grades 90 and over?Which quiz has a greater percentage of students with grades less than 60?Refer to the following information for Questions 11, 12, and 13. There are 1000 students in a high school. Among the 1000 students, 800 students have a laptop, and 300 students have a tablet. 150 students have both devices.What is the probability that a randomly selected student has neither device? (10 pts)What is the probability that a randomly selected student has a laptop, given that he/she has a tablet? (5 pts)Let event A be the selected student having a laptop, and event B be the selected student having a tablet. Are A and B independent events? Why or why not? (5 pts)A combination lock uses three distinctive numbers between 0 and 49 inclusive. How many different ways can a sequence of three numbers be selected? () (5 pts). Let random variable represent the number of heads when a fair coin is tossed three times. (a) Construct a table describing the probability distribution. (5 pts)(b) Determine the mean and standard deviation of . (Round the answer to two decimal places) (10 pts)STAT 200: Introduction to Statistics Final Examination, Fall 2015 OL1/US1 Page 4 of 6Mimi just started her tennis class three weeks ago. On average, she is able to return 20% of heropponents serves. Assume her opponent serves 10 times.(a) Let X be the number of returns that Mimi gets. As we know, the distribution of X is a binomialprobability distribution. What is the number of trials (n), probability of successes (p) andprobability of failures (q), respectively? (5 pts)(b) Find the probability that that she returns at least 1 of the 10 serves from her opponent.() (10 pts)Refer to the following information for Questions 17, 18, and 19. without supporting work, will receive no credit.The lengths of mature jalapeo fruits are normally distributed with a mean of 3 inches and astandard deviation of 1 inch.What is the probability that a randomly selected mature jalapeo fruit is between 1.5 and 4 incheslong? (5 pts)Find the 90th percentile of the jalapeo fruit length distribution. (5 pts)If a random sample of 100 mature jalapeo fruits is selected, what is the standard deviation of thesample mean? (5 pts)A random sample of 100 light bulbs has a mean lifetime of 3000 hours. Assume that thepopulation standard deviation of the lifetime is 500 hours. Construct a 95% confidence intervalestimate of the mean lifetime. (8 pts)Consider the hypothesis test given by: 0.5: 0.510H pH pIn a random sample of 100 subjects, the sample proportion is found to be 0.45 .(a) Determine the test statistic. supporting work, will receive no credit.(b) Determine the -value for this test. without supporting work, will receive no credit.(c) Is there sufficient evidence to justify the rejection of 0 at the 0.01 level?Explain. (15 pts)STAT 200: Introduction to Statistics Final Examination, Fall 2015 OL1/US1 Page 5 of 6Consumption of large amounts of alcohol is known to increase reaction time. To investigate the effects of small amounts of alcohol, reaction time was recorded for five individuals before and after the consumption of 2 ounces of alcohol. Do the data below suggest that consumption of 2 ounces of alcohol increases mean reaction time?Reaction Time (seconds)SubjectBeforeAfter16728834