#50 For each of the following binomial experiments, do the following: a. Find an
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#50
For each of the following binomial experiments, do the following: a. Find and interpret the mean of X. b. Calculate the variance of X. c. Compute the standard deviation of X. 49. Business majors accounted for 25% of the proportion of all Master's degrees granted in 2012. Select three Master's degrees at random. Let X = the number of business majors. 50. The CDC found that 7.5% of children ages 6-17 used prescribed medication during the past six months for emotional or behavioral difficulties. Select four children ages 6-17 at random, and let X = the number of children using prescription medication for emotional or bena difficulties.Explanation / Answer
Given, X is a random variable denoting the number of children using prescription medication for emotional or behavioural difficulties.
Here, X follows a Binomial distribution with n = number of trials = number of children selected at random, aged 6 - 17, p = success probability = probability of finding a child aged 6-17 using prescription medication.
Here, n = 4, p = 0.075 = 7.5%.
(a) the mean of X is given by : E(X) = n * p = 4 * 0.075 = 0.3. This means that out of the 4 selected children, we may find that either no one or a single person may be using prescription medication.
(b) the variance of X is given by : Var(X) = n * p * (1 - p) = 4 * 0.075 * 0.925 = 0.2775.
(c) the standard deviation is given by : SD(X) = square root of Var(X) = square root of 0.2775 = 0.5268.
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