If a fair coin is tossed 100 times,use the normal approximation to estimate the probability of getting at least 60 heads.
A) 0.0287
B) 0.0228
C) 0.0179
D) 0.4713
E) 0.5287

Question

Quizplus · Accepted Answer

We can use the normal approximation to estimate the probability of getting at least 60 heads. We know that the mean of a binomial distribution is np = 100(0.5) = 50 and the standard deviation is sqrt(np(1-p)) = sqrt(100(0.5)(0.5)) = 5.

To use the normal approximation, we need to standardize the value of 60 using the formula z = (x - mu) / sigma, where x is the number of heads, mu is the mean, and sigma is the standard deviation.

z = (60 - 50) / 5 = 2

We can now use a standard normal table or calculator to find the probability of getting a z-score of 2 or more.

Using a standard normal table, we find that P(Z ≥ 2) = 0.0228.

Therefore, the answer is A: 0.0287.

If a Fair Coin Is Tossed 100 Times,use the Normal