ith their root. It Americans are randomly selected, how many Uliets in public t)

Question

ith their root. It Americans are randomly selected, how many Uliets in public t) Co sin ex (g) C e tf 500 adult Americans expect to flush toilets in public restrooms with would we b) Woul Bor? b ush toilets in public restrooms with their foot? their foot? uld it be unusual to observe 280 adult Americans who Would it b ergy Sufferers Clarinex-D is a medication whose purpose 6. Aller duce the symptoms associated with a variety of allergies. is to experienced insomnia as a side effect. (a) If 240 users of Clarinex-D are randomly selected, how many to re in clinical trials of Clarinex-D, 5% of the patients in the study would we expect to experience insomnia as a side effect? b) Would it be unusual to observe 20 patients experiencing insomnia as a side effect in 240 trials of the probability experiment? Why? 47, Spanking In March 1995, The Harris Poll reported that 80% of parents spank their children. Suppose a recent poll of 1030 adult Americans with children finds that 781 indicated that

Explanation / Answer

Q46

Let X = Number of Clarinex-D using patients experiencing insomnia as a side effect.

Then, X ~ B(n, p), ………………………………………………………………………(1) where p = sample size and p = probability of Clarinex-D using patients experiencing insomnia as a side effect, which is also equal to the proportion of Clarinex-D using patients experiencing insomnia as a side effect.

Given 5% of patients in the study experienced insomnia as a side effect, p = 0.05 …….. (2)

Back-up Theory

If X ~ B(n, p). i.e., X has Binomial Distribution with parameters n and p, where n = number of trials and p = probability of one success, then probability mass function (pmf) of X is given by p(x) = P(X = x) = (nCx)(px)(1 - p)n – x, x = 0, 1, 2, ……. , n …………………..(1)

[The above probability can also be directly obtained using Excel Function of Binomial Distribution: BINOMDIST(Number_s:Trials:Probability_s:Cumulative), what is within brackets is (x:n:p:True)] ………………………………………………………………….(1a)

Mean (average) of X = E(X) = np………………………………………………..(2)

Now to work outthe solution:

Part (a)

Expected number of patients experiencing insomnia as a side effect in a sample of 240

= E(X), where X ~ B(240, 0.05)

= 240 x 0.05 [vide (2)]

= 12 ANSWER

Part (b)

To answer this part, probability of finding 20 patients experiencing insomnia as a side effect in a sample of 240

= P(X = 20)

= 0.0088 [1a]

Since the above probability is very low, it is reasonable to assume that it is unusual to observe 20 patients experiencing insomnia as a side effect in a sample of 240. ANSWER

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