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# Statistics: Sampling distribution

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1. All possible sample of size of 150 was collected from a population and listed the sample means for each of these samples.

(a) If the average of the sample means is 450.55 what would be the numerical value of the true population mean. Discuss

(b) If the standard deviation of the sample means is 12.25 determine the standard deviation of the model from which the samples came. Assume the population has a size of 1250.

2. In a bike shop the average repair bill during a maintenance program's first year is \$15.30 with standard deviation of \$7.00

(a) What is the probability a random sample of 40 customers will have a mean repair cost exceeding \$16

(b) What is the probability the mean repair cost for a sample of 100 customers will be between \$15.10 and \$15.80 ( C) The manager offers a spring special. He randomly select and repair the first 50 bikes at \$14 each. He notes this is not even 1 standard deviation below the mean price to make such repairs. He ask your advice. Is this a risky thing to do? Based on the probability ofa repair bill being \$14 or less what would you recommend. Discuss.