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Sampling Distribution of x Worksheet #2 Answers 1a) The probability of the sample of 10 taxi fares would be greater because the variance of the sampling distribution is smaller than the variance of the population causing more area of the distribution to be between $21 & $24. b) The probability of a single taxi fare would be greater because the variance of the population is larger than the variance of the sampling distribution for sample size 10 causing more area of the distribution to be more than $24 2a) The sampling distribution would be approximately normal because of the large sample size. b) μ x 6, σ x .3536 c) P (x 5) .0023 - Yes, this indicates that the manufacturing process is faulty because it is not likely that a sample of 50 have a mean weight of 5 ounces or less. d) The sampling distribution of sample size 100 would have less variance and be taller & thinner. 3a) μ 157, σ 3 b) P (x 155.7) .3324 c) The sampling distribution is normally distributed with x 157 and x .4743 d) P (x 155.7) .0031 e) In order to reduce the standard deviation by 50%, the sample size must increase 4 times. 4a) 150 pounds b) 6.75 pounds c) 156.25 pounds d) P (x 156.25) .1772