Answer:
a) the expected number of tweets with no reaction is 71 tweets
b) the variance is 20.59 tweets² ( ≈ 21 tweets )and the standard deviation is
4.537 tweets (≈ 5 tweets)
Step-by-step explanation:
we can use the binomial probability distribution
P(x, N, p ) = N!/[(N-x)!x!] * p^x * (1-p)^(N-x)
where
x = number of successful events
N = population total
p = probability for success for every individual and independent event
P = probability for x successful events
in our case p = 71% = 71/100 (probability of a tweet without reaction) , N = 100 tweets
a) the expected number of tweets
E(x) = N* p = 100 tweets * 71/100 = 71 tweets
b) the variance is
V(x) = N * p * (1-p)
V = 100 * 71/100 * (1-71/100) = 71* 29/100 = 20.59 tweets² ( units of variance are [N²] )
the standard deviation is
s = √V = √20.59 tweets² = 4.537 tweets
