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Mean of Occurring Population

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The mean of a population is 76 and the standard deviation is 14. The shape of the population is unknown. Determine the probability of each of the following occuring from this population.

a. A random sample of size 35 yielding a sample mean of 79 or more

b. A random sample of size 140 yielding a sample mean of between 74 and 77

c. A random sample of size 219 yielding a sample mean of less than 76.5

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Solution Summary

The shape of the population is unknown. The probability is determined for multiple random samples.

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The mean of a population is 76 and the standard deviation is 14. The shape of the population is unknown. Determine the probability of each of the following occuring from this population.

a. A random sample of size 35 yielding a sample mean of 79 or more

We can use the law of Large Numbers. Denote by Xbar the sample mean with sample size n=35. Then Xbar ...

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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