Question

if a binomial trial has a probability of success of 0.3, how many successes would you expect out of 2000 trials?

choice

a. 1800
b. 1400
c. 1000
d. 600

Explanation:

Step1: Recall the formula for the expected value in a binomial distribution

The expected number of successes \( E(X) \) in a binomial distribution is given by the formula \( E(X)=n\times p \), where \( n \) is the number of trials and \( p \) is the probability of success on a single trial.

Step2: Identify the values of \( n \) and \( p \)

In this problem, the number of trials \( n = 2000 \) and the probability of success \( p=0.3 \).

Step3: Calculate the expected number of successes

Substitute the values of \( n \) and \( p \) into the formula: \( E(X)=2000\times0.3 \).
Calculating \( 2000\times0.3 \), we get \( 600 \).

Answer:

D. 600