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Standard deviation and probability.

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In 1851 there were 25,466 nurses in Great Britain.

Age Range Yrs 20-29 30-39 40-49 50-59 60-69 70-79 80-89
Midpoint X 24.5 34.5 44.5 54.5 64.5 74.5 84.5
Percent of Nurses 5.7 9.7 19.5 29.2 25.0 9.1 1.8

I have three parts to this question that is similar to one I am working on, Please detail how you do this:

1) Find the probability that a British nurse selected at random in 1851 would be 60 years or older. (My guess is The sum of the percent of nurses 60 years are older are added equaling 36% or 1967.76/25466) am I even close?
2) Compute he expected age µ of a British nurse contemporary.
3) Compute the standard deviation α for the ages of the nurses shown.

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The solution examines standard deviation and probability.

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Standard deviataion and probability.
________________________________________
In 1851 there were 25,466 nurses in Great Britain.

Age Range Yrs 20-29 30-39 40-49 50-59 60-69 70-79 80-89
Midpoint X 24.5 34.5 44.5 54.5 64.5 74.5 84.5
Percent of Nurses 5.7 9.7 19.5 29.2 25.0 9.1 1.8 ...

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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