Question Solved1 Answer Scores on a Statistics final are normally distributed, with a mean of 78 and a standard deviation of 12. A student takes his final; find the probability that the student gets a score is less than 71. Then, find the probability that the student score at least a 95. The probability that the student scores less than 71 is A The probability that the student scores are 95 or more is BT

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Transcribed Image Text: Scores on a Statistics final are normally distributed, with a mean of 78 and a standard deviation of 12. A student takes his final; find the probability that the student gets a score is less than 71. Then, find the probability that the student score at least a 95. The probability that the student scores less than 71 is A The probability that the student scores are 95 or more is BT
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Transcribed Image Text: Scores on a Statistics final are normally distributed, with a mean of 78 and a standard deviation of 12. A student takes his final; find the probability that the student gets a score is less than 71. Then, find the probability that the student score at least a 95. The probability that the student scores less than 71 is A The probability that the student scores are 95 or more is BT
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Answer: We know when x∼N(mu,sigma^(2)) then (x-mu)/(sigma)∼N(0,1)let x be scores on statistics finalX⇝N(78,(12)^(2))We have to find P[x < 71] and P[x⩾95]{:[P[x < 71],=P[(x-mu)/(sigma) < (71-mu)/(sigma)]],[,=P[z < (71-78)/(12)],],[,=P[z < -0.5833],],[,=0.2798,:'" from standard ... See the full answer