ST 201 Recitation Activity Week 7 Sampling Distributions & The Central Limit The

Question

ST 201 Recitation Activity Week 7 Sampling Distributions & The Central Limit Theorem Objective The focus of today's recitation will be to work through practice problems which require knowledge of sampling distributions and the Central Limit Theorem. Example 1: A car insurance company looks at the records for thousands of car owners and determines that the mean loss from collisions in a year is = $750 per person. The company plans to sell collision insurance for $750 plus enough to cover its costs and expenses. Explain why it would be unwise to sell only 10 policies. Explain why selling thousands of policies is a safe business practice. The population distribution of a variable is the distribution of values of the variable among all the individuals in the population. The sampling distribution of a statistic is the distribution of values taken by the statistic in all possible samples of the same size from the same population. Example 2 During World War II, 12,000 able-bod required physical training. Each student ran a mean 7. mean time i = 7.15 minutes. A second random sample of size 100 has mean x-697 minutes. After many random samples, the values of the many samples means (x) follow the normal distribution with mean 7.11 minutes and standard deviation 0.074 minutes ed male undergraduates at the University of Illinois participated in timed mile. Their times followed a normal distribution with 11 minutes and standard deviation 0.74 minutes. A random sample of 100 of these students has What is the population being described above? Describe the population distribution. How can one interpret that population mean and standard deviation in the context of this problem? a.

Explanation / Answer

Based on the central limit theorum , we know that when the sample size is large the mean tends to be closer to the population mean . if the sample size is too small then the sample mean tends to stay away from the population mean

so if n = 10 , then the sampling distribution would be different

however if the sample size is large , then the sampling distribution tends to follow the population distribution

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