Use the appropriate normal distribution to approximate the resulting binomial distribution.
A fair coin is tossed 25 times. What is the probability of obtaining more than 12 heads? (Round your intermediate calculations to 2 decimal places.)

A) 0.1587
B) 0.6214
C) 0.5793
D) 0.6316
E) 0.1738

Question

Use the appropriate normal distribution to approximate the resulting binomial distribution. ​
A fair coin is tossed 25 times. What is the probability of obtaining more than 12 heads? (Round your intermediate calculations to 2 decimal places.)
​
A) 0.1587
B) 0.6214
C) 0.5793
D) 0.6316
E) 0.1738

Quizplus · Accepted Answer

The binomial distribution can be approximated by a normal distribution when n is large. Here, n = 25 and p = 0.5. The mean (μ) is np = 12.5 and the standard deviation (σ) is √(np(1-p)) = √6.25 = 2.5. Using the normal approximation, P(X > 12) is calculated using the z-score and standard normal distribution tables, resulting in approximately 0.5793.

Use the Appropriate Normal Distribution to Approximate the Resulting Binomial