Answer:
(1) The correct option is (A).
(2) The probability that Aadi will get Tails is [tex]\frac{2}{5}[/tex].
Step-by-step explanation:
It is provided that:
- Eric throws a biased coin 10 times. He gets 3 tails.
- Sue throw the same coin 50 times. She gets 20 tails.
The probability of tail in both cases is:
- [tex]P(\text{Tail})=\frac{3}{10}[/tex]
- [tex]P(\text{Tail})=\frac{20}{50}=\frac{2}{5}[/tex]
(1)
According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.
In this case we need to compute the proportion of tails.
Then according to the Central limit theorem, Sue's estimate is best because she throws it n = 50 > 30 times.
Thus, the correct option is (A).
(2)
As explained in the first part that Sue's estimate is best for getting a tail, the probability that Aadi will get Tails when he tosses the coin once is:
[tex]P(\text{Tail})=\frac{20}{50}=\frac{2}{5}[/tex]
Thus, the probability that Aadi will get Tails is [tex]\frac{2}{5}[/tex].
