A binomial distribution has 50 trials (n = 50) with a probability of success of 0.50 ($\pi$=0.50). To use the normal distribution to approximate the binomial, what are the mean and standard deviation?
A) µ = 25 and $\sigma$ = 3.5355
B) µ =25 and $\sigma$ = 12.5
C) µ =25 and $\sigma$ = 4.33
D) µ =50 and $\sigma$ = 100

Question

A binomial distribution has 50 trials (n = 50) with a probability of success of 0.50 ($\pi$=0.50). To use the normal distribution to approximate the binomial, what are the mean and standard deviation?
A) µ = 25 and $\sigma$ = 3.5355
B) µ =25 and $\sigma$ = 12.5
C) µ =25 and  $\sigma$ = 4.33
D) µ =50 and  $\sigma$ = 100

Quizplus · Accepted Answer

According to the normal approximation to the binomial distribution, the mean of the normal distribution is equal to the mean of the binomial distribution (µ = np = 50 × 0.50 = 25) and the standard deviation of the normal distribution is equal to the square root of the product of the number of trials, the probability of success, and the probability of failure (σ = sqrt(np(1-p)) = sqrt(50 × 0.50 × 0.50) = 3.5355). Therefore, option A is the best choice.

A Binomial Distribution Has 50 Trials (N = 50) with a Probability