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Finding probabilities based on a sample

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The owner of Britten's Egg Farm wants to estimate the mean number of eggs laid per chicken. A sample of 20 chickens shows they laid an average of 20 eggs per month with a standard deviation of 2 eggs per month.

a. what is the value of the population mean? what is the best estimate of this value?
b. explain why we need to use the t distribution. what assumption do yo uneed to make?
c. for a 95 percent confidence interval, what is the value of t?
d. develop the 95 percent confidence interval for the population mean
e. would it be reasonable to conclude that the population mean is 21 eggs? what about 25 eggs?
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Details: A normal distribution has a mean of 50 and a standard deviation of 4.
a. compute the probability of a value between 44.0 and 55.0
b. compute the probability of a value greater than 55.0
c. compute the probability of a value between 52.0 and 55.0

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The solution contains detailed explanation of finding probabilities based on a sample from a normal distribution.

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ect: normal distribution & standard deviation
Details: A normal distribution X has a mean of 50 and a standard deviation of 4.
a. compute the probability of a value between 44.0 and 55.0
Solution. Using the following website, you can compute these probabilities.
http://people.hofstra.edu/faculty/Stefan_Waner/RealWorld/stats/normaldist.html

P(44.0<=X<=55.0)=0.827541

b. compute the probability of a value greater than 55.0
Solution. Using the following website, you can compute these probabilities.
http://people.hofstra.edu/faculty/Stefan_Waner/RealWorld/stats/normaldist.html

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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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