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:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
The probability of a head is 0.27.
This means that the probability of tails is [tex]p = 1 - 0.27 = 0.73[/tex]
The coin is thrown 200 times.
This means that [tex]n = 200[/tex]
Write an estimate for the amount of tails
This is the expected value, so:
[tex]E(X) = np = 200*0.73 = 146[/tex]
The estimate for the amount of tails is 146.
