Answer: b) 84
Step-by-step explanation:
Let p be the prior estimate of the required proportion.
As per given , we have
p =0.5 (The probability of getting heads on a fair coin is 0.5)
Significance level : [tex]\alpha: 1-0.90=0.10\\[/tex]
Critical z-value (using z-value table ) : [tex]z_{\alpha/2}=1.645[/tex]
Confidence interval width : w= 0.18
Thus , the margin of error : [tex]E=\dfrac{w}{2}=0.09[/tex]
Formula to find the sample size ( if prior estimate of proportion is known.):-
[tex]n=p(1-p)(\dfrac{z_{\alpha/2}}{E})^2[/tex]
Substitute the values , we get
[tex]n=0.5(1-0.5)(\dfrac{1.645}{0.09})^2[/tex]
Simplify ,
[tex]n=83.5192901235\approx84[/tex] [Round of to the next whole number.]
Hence, the number of times we would have to flip the coin =84
hence, the correct answer is b) 84
