Answer:
a. 4.33.
Step-by-step explanation:
If there is only one correct answer out of four alternatives, the expected proportion of correct answers is p =0.25
Sample size (n) = 100 questions
The standard deviation of a proportion 'p' is given by:
[tex]s=\sqrt{\frac{p*(1-p)}{n} }[/tex]
Applying the given data:
[tex]s=\sqrt{\frac{0.25*(1-0.25)}{100}}\\s=0.0433[/tex]
If X is the number of correct responses in 100 guesses, the standard deviation of X is:
[tex]\sigma = n*s=100*0.0433\\\sigma = 4.33[/tex]
The standard deviation of X is 4.33 questions.
