g A coin where the probability of heads is 0.3 is flipped 2000 times. Use the normal approximation to the binomial distribution

Question

3 years ago

7

to find the probability of getting between 575 and 618 heads (inclusive).

1 answer:

matrenka [14] · Answer 1 · 2022-04-30T08:57:45+03:00

Title:

<h2>See the explanation.</h2>

Step-by-step 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 $^{2000}C_n (0.3)^n \times (0.7)^{2000 - n}$ .

The required probability is ∑ $^{2000}C_n (0.3)^n \times (0.7)^{2000 - n}$ , where $575 \leq n \leq 618$ .