Question

Refer to the previous Check Your Understanding (page 390 ) about Mrs. Desai's special multiple-choice quiz on binomial distributions. We defined $X=$the number of Patti's correct guesses.

1. Find ${\mu }_X$. Interpret this value in context.

2. Find localid="1649452775386" ${\sigma }_X$. Interpret this value in context.

Short answer

The standard deviation value of${\sigma }_X$is$1.265$

Step-by-step solution

Given Information 

Number of questions$=10$

Students are supposed to guess the answers.

$X$is a number of answers that Patti gives correct.

Probability of success$\left(p\right)=0.2$

Explanation

Compute the mean using binomial distribution is:

${\sigma }_X=\sqrt{n\times p\times (1-p)}$

Calculation:

The standard deviation of $X$is computed as:

localid="1649854842527" $$\begin{gathered} {\sigma }_X=\sqrt{n\times p\times (1-p)} \\ =\sqrt{10\left(0.2\right)(1-0.2)} \\ =1.265 \end{gathered}$$.