Question

a university found that 30% of its students withdraw without completing the introductory statistics course. assume that 20 students registered for the course. (round your answers to four decimal places.) (a) compute the probability that two or fewer will withdraw. (b) compute the probability that exactly four will withdraw. (c) compute the probability that more than three will withdraw. (d) compute the expected number of withdrawals. 8. 2 / 3 points according to a 2010 study conducted by the toronto - based social media analytics firm sysomos, 71% of all tweets get no reaction. that is, these are tweets that are not replied to or retweeted. suppose we randomly select 500 tweets. (a) what is the expected number of these tweets with no reaction? (b) what are the variance and standard deviation for the number of these tweets with no reaction? (round your answer for the standard deviation to four decimal places.) variance standard deviation

Explanation:

Step1: Recall the formula for standard deviation of a binomial distribution

For a binomial distribution with parameters \( n \) (number of trials) and \( p \) (probability of success), the variance \( \sigma^2 = np(1 - p) \) and the standard deviation \( \sigma=\sqrt{np(1 - p)} \).

We know that \( n = 500 \) and \( p=0.71 \), so \( 1 - p = 1 - 0.71=0.29 \). The variance is given as \( np(1 - p)=500\times0.71\times0.29 = 102.95 \) (which matches the provided variance).

Step2: Calculate the standard deviation

To find the standard deviation, we take the square root of the variance. So we need to compute \( \sigma=\sqrt{102.95} \).

Using a calculator, \( \sqrt{102.95}\approx10.1464 \) (rounded to four decimal places).

Answer:

\( 10.1464 \)