Answer:
The estimate for the amount of tails is 146.
Step-by-step explanation:
For each throw, there are only two possible outcomes. Either it is a head, or it is tails. Throws are independent. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
![E(X) = np](https://tex.z-dn.net/?f=E%28X%29%20%3D%20np)
The standard deviation of the binomial distribution is:
![\sqrt{V(X)} = \sqrt{np(1-p)}](https://tex.z-dn.net/?f=%5Csqrt%7BV%28X%29%7D%20%3D%20%5Csqrt%7Bnp%281-p%29%7D)
The probability of a head is 0.27.
This means that the probability of tails is ![p = 1 - 0.27 = 0.73](https://tex.z-dn.net/?f=p%20%3D%201%20-%200.27%20%3D%200.73)
The coin is thrown 200 times.
This means that ![n = 200](https://tex.z-dn.net/?f=n%20%3D%20200)
Write an estimate for the amount of tails
This is the expected value, so:
![E(X) = np = 200*0.73 = 146](https://tex.z-dn.net/?f=E%28X%29%20%3D%20np%20%3D%20200%2A0.73%20%3D%20146)
The estimate for the amount of tails is 146.