Question 617683: In the Department of Education at UR University, student records suggest that the population of students spends an average of 5.5 hours per week playing organized sports. The population’s standard deviation is 2.2 hours per week. Based on a sample of 121 students, Healthy Lifestyles Incorporated (HLI) would like to apply the central limit theorem to make various estimates.
Calculate that the probability that the sample mean will be between 5.3 and 5.7 hours.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! In the Department of Education at UR University, student records suggest that the population of students spends an average of 5.5 hours per week playing organized sports. The population’s standard deviation is 2.2 hours per week. Based on a sample of 121 students, Healthy Lifestyles Incorporated (HLI) would like to apply the central limit theorem to make various estimates.
Calculate that the probability that the sample mean will be between 5.3 and 5.7 hours.
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z(5.3) = (5.3-5.5)/[2.2/sqrt(121)] = -1
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z(5.7) = (5.7-5.5)/(2.2/sqrt(121)] = +1
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P(5.3< x-bar <5.7) = P(-1< z < 1) = 0.6827
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Cheers,
Stan H.
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