How Much Do Clicks Wobble?

Probability DistributionsMedium+20 XP+20

How Much Do Clicks Wobble?

A marketing team sends out $200$ emails. The emails behave independently of one another, and for each single email:

it is opened with probability $0.15$ ;
if it is opened, it then leads to a click with probability $0.20$ ;
an email that is never opened can never be clicked.

Let $X$ be the number of the $200$ emails that end up clicked.

What is the standard deviation of $X$ ?

Round to two decimal places.

Hints

clicks

Binomial Distribution

Number of Trials (n):10

Success Prob. (p):0.50

Successes (k):5

Properties & Formula

Formula: C(n,k)·pᵏ·(1-p)ⁿ⁻ᵏ

n = 10, p = 0.50, k = 5

C(10,5) = 252

P(X = 5) = 0.2461

E[X] = np = 5.00

Var(X) = np(1-p) = 2.500

A Binomial Distribution counts the number of successes in n independent trials.
As n increases, the binomial distribution looks more symmetric and bell-shaped regardless of p. That is an early glimpse of the Central Limit Theorem.

The Binomial Distribution models independent Bernoulli trials. It assumes a fixed number of trials n and a constant success probability p. Its expected value is np and its variance is np(1-p).

How Much Do Clicks Wobble?