Question

g A coin where the probability of heads is 0.3 is flipped 2000 times. Use the normal approximation to the binomial distribution to find the probability of getting between 575 and 618 heads (inclusive).

Answer 1

Title:

See the explanation.

Explanation:

The coin is to be flipped 2000 times.

The probability of getting a head is 0.3.

It is given that, we need to get a head in between 575 and 618 times.

If we will get 575 heads then we will get (2000 - 575) tails.

Hence, if we take that we want to get n times head, then we will get (2000 - n) times tail.

The probability of not getting a head is (1 - 0.3) = 0.7.

The probability of getting n times head is
`^(2000)C_n (0.3)^n * (0.7)^(2000 - n)`.

The required probability is ∑
`^(2000)C_n (0.3)^n * (0.7)^(2000 - n)`, where
`575 \leq n \leq 618`.