Random Sample of Individuals with Sinusitis Relief
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Vaccinations are effective in treating sinusitis (inflammation of the membrane lining the facial sinuses) in individuals predisposed to allergies. Specifically, the researchers reported that 98% of individuals predisposed to allergies find relief from their sinusitis after allergy vaccinations. Suppose that this number is accurate and that 120 individuals predisposed to allergies are chosen at random and given allergy vaccinations.
a. Estimate the number of individuals in the random sample who do not find relief from their sinusitis by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable). Do not round your response.
b. Quantify the uncertainty of your estimate by giving the standard deviation of the distribution. Round your response to at least three decimal places.
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Solution Summary
Vaccinations are effective in treating sinusitis (inflammation of the membrane lining the facial sinuses) in individuals predisposed to allergies. Specifically, the researchers reported that 98% of individuals predisposed to allergies find relief from their sinusitis after allergy vaccinations. Suppose that this number is accurate and that 120 individuals predisposed to allergies are chosen at random and given allergy vaccinations.
a. Estimate the number of individuals in the random sample who do not find relief from their sinusitis by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable). Do not round your response.
b. Quantify the uncertainty of your estimate by giving the standard deviation of the distribution. Round your response to at least three decimal places.
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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