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 : ![\alpha: 1-0.90=0.10\\](https://tex.z-dn.net/?f=%5Calpha%3A%201-0.90%3D0.10%5C%5C)
Critical z-value (using z-value table ) : ![z_{\alpha/2}=1.645](https://tex.z-dn.net/?f=z_%7B%5Calpha%2F2%7D%3D1.645)
Confidence interval width : w= 0.18
Thus , the margin of error : ![E=\dfrac{w}{2}=0.09](https://tex.z-dn.net/?f=E%3D%5Cdfrac%7Bw%7D%7B2%7D%3D0.09)
Formula to find the sample size ( if prior estimate of proportion is known.):-
![n=p(1-p)(\dfrac{z_{\alpha/2}}{E})^2](https://tex.z-dn.net/?f=n%3Dp%281-p%29%28%5Cdfrac%7Bz_%7B%5Calpha%2F2%7D%7D%7BE%7D%29%5E2)
Substitute the values , we get
![n=0.5(1-0.5)(\dfrac{1.645}{0.09})^2](https://tex.z-dn.net/?f=n%3D0.5%281-0.5%29%28%5Cdfrac%7B1.645%7D%7B0.09%7D%29%5E2)
Simplify ,
[Round of to the next whole number.]
Hence, the number of times we would have to flip the coin =<u>84</u>
hence, the correct answer is b) 84
Might be 1? Because it is 100 each