Answer:
[tex]Mean = 12[/tex]
[tex]Standard\ Deviation = 6[/tex]
Step-by-step explanation:
Given
Number of questions, n = 48
Probability of correct answer, p = 1/4
Required
- Find the mean
- Find the standard deviation
Using probability notations;
n = 48 and p = 1/4
Mean is calculated as follows;
[tex]Mean = np[/tex]
Substitute 48 for n and 1/4 for p
[tex]Mean = 48 * \frac{1}{4}[/tex]
[tex]Mean = \frac{48}{4}[/tex]
[tex]Mean = 12[/tex]
The Mean is 12
Calculating Standard Deviation (SD)
[tex]SD = \sqrt{np(1-p)}[/tex]
Substitute 48 for n and 1/4 for p
[tex]SD = \sqrt{48 * \frac{1}{4}(1-\frac{1}{4})}[/tex]
Solve the expression in the bracket
[tex]SD = \sqrt{48 * \frac{1}{4}(\frac{4-1}{4})}[/tex]
[tex]SD = \sqrt{48 * \frac{1}{4}(\frac{3}{4})}[/tex]
Open Bracket
[tex]SD = \sqrt{48 * \frac{1}{4}*\frac{3}{4}}[/tex]
[tex]SD = \sqrt{\frac{48 * 1 * 3}{4}}[/tex]
[tex]SD = \sqrt{\frac{144}{4}}[/tex]
[tex]SD = \sqrt{36}[/tex]
Take Square Root of 36
[tex]SD = 6[/tex]
The standard deviation is 6
