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Probabilities from proportion tables

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The following tables give the proportions of men and women in the U S population, and the proportions of men and women who have never married, in a recent year.
men
age proportion in population proportion never married
18-24 0.133 0.874
25-34 0.205 0.397
35-44 0.232 0.187
45-64 0.287 0.075
65 or over 0.142 0.038

women
age proportion in population proportion never married
18-24 0.123 0.775
25-34 0.194 0.298
35-44 0.219 0.121
45-64 0.284 0.062
65 or over 0.181 0.047
Find the probability that a randomly selected man who has never married is between 35 and 44 years old (inclusive)

Find the probability that a randomly selected woman who has been married is between 18 and 24 (inclusive)

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Solution Summary

Probabilities are calculated from a proportion table. The proportion of males and female who are not married between the age of 35 and 44 years old are determined.

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Solution. Let A1, A2,A3,A4 and A5 denote the event that a person is man with age 18-24, 25-34,35-44,45-64, and 65 or over, respectively.
Let B1, B2,B3,B4 and B5 denote the event that a person is woman with age 18-24, 25-34,35-44,45-64, and 65 or ver, respectively. We denote the event that a man never marries by AC, and a woman never marries by BC, and we denote the event that a ...

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
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  • "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!"
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