Suppose you sample one value from a uniform distribution with a = 0 and b = 10. a. What is the probability that the value will be between 6 and 9? b. What is the probability that the value will be between 2 and 4? c. What is the mean? d. What is the standard deviation? . . . a. The probability that the value will be between 6 and 9 is (Type an integer or a decimal.) b. The probability that the value will be between 2 and 4 is (Type an integer or a decimal.) c. The mean of the given uniform distribution is u = (Type an integer or a decimal.) d. The standard deviation of the given uniform distribution is o = (Round to four decimal places as needed.)The major stock market indexes had strong results in a recent year. The mean one-year return for stocks i Index A, a group of very large companies, was 10.2%. The mean one-year return for stocks in Index B, a group of small and medium-sized companies, was 11.8%. Historically, the one-year returns are approximately normally distributed, the standard deviation in Index A is approximately 15%, and the standard deviation in Index B is approximately 35%. Complete parts (a) through (f) below. a. What is the probability that a stock in Index A gained value in this year? (Round to four decimal places as needed.) b. What is the probability that a stock in Index A gained 20% or more in this year? (Round to four decimal places as needed.) c. What is the probability that a stock in Index A lost 15% or more in this year? (Round to four decimal places as needed.) d. What is the probability that a stock in Index A lost 35% or more in this year? (Round to four decimal places as needed.) e. Repeat (a) through (d) for a stock in Index B. What is the probability that a stock in Index B gained value in this year? (Round to four decimal places as needed.) What is the probability that a stock in Index B gained 20% or more in this year? (Round to four decimal places as needed.) What is the probability that a stock in Index B lost 15% or more in this year? (Round to four decimal places as needed.) What is the probability that a stock in Index B lost 35% or more in this year? (Round to four decimal places as needed.) f. Write a short summary on your findings. Be sure to include a discussion of the risks associated with a large standard deviation. Choose the correct answer below. O A. While stocks in Index B have a higher mean one-year return and a higher probability of a gain than stocks in Index A, due to the greater variation of Index B, they also have a higher probability of sustaining large losses of 35% or more. O B. While stocks in Index B have a higher mean one-year return than stocks in Index A, they have a lower probability of a large nain of 20% or more or a large loss of 15% or more due to their t more help - NextThe major stock market indexes had strong results in a recent year. The mean one-year return for (Round to four decimal places as needed.) c. What is the probability that a stock in Index A lost 15% or more in this year? (Round to four decimal places as needed.) d. What is the probability that a stock in Index A lost 35% or more in this year? (Round to four decimal places as needed.) e. Repeat (a) through (d) for a stock in Index B. What is the probability that a stock in Index B gained value in this year? (Round to four decimal places as needed.) What is the probability that a stock in Index B gained 20% or more in this year? (Round to four decimal places as needed.) What is the probability that a stock in Index B lost 15% or more in this year? (Round to four decimal places as needed.) What is the probability that a stock in Index B lost 35% or more in this year? (Round to four decimal places as needed.) f. Write a short summary on your findings. Be sure to include a discussion of the risks associated with a large standard deviation. Choose the correct answer below. O A. While stocks in Index B have a higher mean one-year return and a higher probability of a gain than stocks in Index A, due to the greater variation of Index B, they also have a higher probability of sustaining large losses of 35% or more. O B. While stocks in Index B have a higher mean one-year return than stocks in Index A, they have a lower probability of a large gain of 20% or more or a large loss of 15% or more due to their greater variation. O C. While stocks in Index B have a higher mean one-year return and a higher probability of a gain than stocks in Index A, due to the greater variation of Index B, they have a lower probability of a large gain of 20% or more. O D. While stocks in Index B have a higher mean one-year return and a higher probability of a large gain of 20% or more than stocks in Index A, due to the greater variation of index B, they also have a higher probability of sustaining large losses of 15% or more.Suppose that the commuting time on a particular train is uniformly distributed between 49 and 59 minutes. a. What is the probability that the commuting time will be less than 51 minutes? b. What is the probability that the commuting time will be between 51 and 56 minutes? c. What is the probability that the commuting time will be greater than 51 minutes? d. What are the mean and standard deviation of the commuting time? a. The probability that the commuting time will be less than 51 minutes is (Type an integer or a decimal.) b. The probability that the commuting time will be between 51 and 56 minutes is (Type an integer or a decimal.) c. The probability that the commuting time will be greater than 51 is (Type an integer or a decimal.) d. The mean of the given uniform distribution is u = (Type an integer or a decimal.) The standard deviation of the given uniform distribution is o = (Round to four decimal places as needed.)A set of final examination grades in an introductory statistics course is normally distributed, with a mean of 75 and a standard deviation of 8. Complete parts (a) through (d). a. What is the probability that a student scored below 89 on this exam? The probability that a student scored below 89 is (Round to four decimal places as needed.) b. What is the probability that a student scored between 67 and 96? The probability that a student scored between 67 and 96 is (Round to four decimal places as needed.) c. The probability is 5% that a student taking the test scores higher than what grade? The probability is 5% that a student taking the test scores higher than Round to the nearest integer as needed.) d. If the professor grades on a curve (for example, the professor could give A's to the top 10% of the class, regardless of the score), is a student better off with a grade of 91 on the exam with a mean of 75 and a standard deviation of 8 or a grade of 65 on a different exam, where the mean is 61 and the standard deviation is 4? Show your answer statistically and explain. A student is with a grade of 91 on the exam with a mean of 75 and a standard deviation of 8 because the Z value for the grade of 91 is and the Z value for the grade of 65 on the different exam is 'Round to two decimal places as needed.)