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 140 individuals predisposed to allergies are chosen at random and given allergy vaccinations.

answer the following.

(if necessary, consult a list of formulas.)

(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.

Explanation:

Identify the parameters of the distribution

Using the Failure Rate Calculation knowledge point

$$
LATEXBLOCK0
$$

Calculate the expected value (mean)

Using the Binomial Mean knowledge point

$$
LATEXBLOCK1
$$

Calculate the standard deviation

Using the Binomial Standard Deviation knowledge point

$$
LATEXBLOCK2
$$

Round the standard deviation

Using the Binomial Standard Deviation knowledge point

$$ \sigma \approx 1.657 $$

Answer:

Question 1

2.8

Question 2

1.657