Question

At a recent meeting at the American College of Asthma, Allergy, and Immunology, researchers reported that allergy 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 150 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).
B. Quantify the uncertainty of your estimate by giving the standard deviation of the distribution.

Answer 1

Here we can use the Binomial distribution, as there are only two possible outcomes.

The given data:

n = 150

q = 98%

= 0.98

p = probability of not finding relief = 1 - 0.98

= 0.02

A). The number of the individuals who do not find any relief from sinusitis is :

E(x) = np

= 150 x 0.02

= 3

B). The uncertainty of my estimate is =
`$√(npq)$`

`$=√(150 * 0.02 * 0.98)$`

= 1.716