1. [-12 Points] DETAILS BBBASICSTATS 6.1.003. Consider each distribution. Determine if it is a valid probability distribution or not, and explain your answer. (a) x O 1 2 PE) 0.24 0.65 0.11 0 Yes. The probabilities do not sum to 1. 0 Yes. The probabilities sum to 1. O No. The probabilities do not sum to 1. O No. The probabilities sum to .1. (b) x 0 1 2 P(X) 0.24 0.65 0.16 O No. The probabilities sum to 1. 0 Yes. The probabilities do not sum to 1. 0 Yes. The probabilities sum to 1. O No. The probabilities do not sum to 1. Submit Answer 2. [-12 Points] BBBASICSTATB 6.1 .001MI. Consider the probability distribution shown below. x o 1 2 pm 0.05 0.50 0.45 Compute the expected value of the distribution. : Compute the standard deviatioh of the distribution. (Round your answer to four decimal places.) E Consider a binomial experlment with n e 4 trials where the probahlllty of success on a single trial is p e 0.20. (Rnund your answers to three decimal places ) USES (a) Flnd P(r: o). (b) Find pfr e l) by using the complement rule. BE BASICSTATB 6i2t016tM | 5' ASK VOUR TEACHER Richard has just been given a quuestlon multiplechulce qulZ in his history class. Each question has ve answers, of which only one is correct. S'lnce Richard has not attended class recently, he duesn't know any of the answers. Assuming that Richard guesses on all eight questions, nd the indicated probabilities. (Round your answers to three decimal places.) USES (a) what is the probability that he will answer all questions carrectly" S (b) what is the probability that he will answer all questions incorrectly? (c) what is the probability that he will answer at least one of the questions correctlyr Compute this probability two ways, First, use the rule for mutually exclusive euents and the probabilities shown in the binomial probability distribution table. S Then use the fact that P(r e 1) : 1 a P(r : o). S Compare the two results. should they be equal? Are they equal? if not, how do you account for the difference? 4. [l6 Paints] 0 They should be equal, but may not be due to table error. 0 They should be equal, but may differ slightly due to rounding ermn 0 They should not be equal, but are equal. 0 They should be equal, but differ substantially. (d) what is the probability that Richard will answer at least half the questions correctly? E 5. [-!2 Points] I DETAILS I BBBASICSTATS 7.2.004. What are the values of the mean and standard deviation of a standard normal distribution? a = E 6. [-14 Points] DETAILS BBBASICSTATS 7.2.005.MI. A normal distribution has _u = 30 and 0' = 5. (a) Find the z score corresponding to x = 25. S (b) Find the 2 score corresponding to x = 44. S (c) Find the raw score corresponding to z = 3. E (d) Find the raw score corresponding to z = 1.7. E 7. [-31 Points] DETAILS BBBASICSTATS 7.2.0165. Sketch the area under the standard normal curve over the indicated interval and nd the specied area. (Round your answer to four decimal places.) Ia USE SALT The area to the left of z = 0.50 is S