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Question: Average score of the students in a statistics contest is 65, and the standard deviation is 15. If a random sample of 16 students who participated in the contest are selected, then find the probability that the sample mean of the scores lies between 61 and 67. Steps to derive 1 Since the variable is approximately normally distributed, the distribution of sample means will be approximately normal with a mean of 65.2 Let X ‾ 3 The standard deviation of the sample mean is σ X ‾ σ n 1 5 1 6 4 The problem is to find P(61 < X ‾ 5 = P(6 1 - 6 5 1 5 / 1 6 X ‾ - μ σ / n 6 7 - 6 5 6 5 / 1 6 z X ‾ 6 = P(- 1.07 < z z 7 The probability that the sample mean of the scores in statistics contest lies between 61 and 67 is 56.02%.Hence the right answer is Option C Click Here To Go Back The number of watches sold per day are: 11, 18, 15, 16, 15. Find the range and mean... The number of hours of study of a student per day is: 5, 3, 8, 4, 10, 6. Find the range a.. 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