Question

a die is rolled nine times and the number of times that two shows on the upper face is counted. if this experiment is repeated many times, find the mean for the number of twos.

a. 1.5 twos
b. 7.5 twos
c. 3 twos
d. 2.25 twos

Explanation:

Step1: Identify probability of getting 2

The probability $p$ of getting a 2 when rolling a fair - six - sided die is $p=\frac{1}{6}$.

Step2: Identify number of trials

The number of trials $n$ is $n = 9$.

Step3: Use mean formula for binomial distribution

The mean $\mu$ of a binomial distribution is given by $\mu=np$. Substitute $n = 9$ and $p=\frac{1}{6}$ into the formula: $\mu=9\times\frac{1}{6}=\frac{9}{6}=1.5$.

Answer:

A. 1.5 twos