A binomial distribution has p = 1/5 and q = 4/5 with n = 100.In the normal approximation to this distribution,what is the z-score corresponding to X = 25?
A)z = 0.50
B)z = 1.00
C)z = 1.25
D)z = 1.50

Question

A binomial distribution has p = 1/5 and q = 4/5 with n = 100.In the normal approximation to this distribution,what is the z-score corresponding to X = 25?​
A)​z = 0.50
B)​z = 1.00
C)​z = 1.25
D)​z = 1.50

Quizplus · Accepted Answer

To find the z-score corresponding to X = 25 in the normal approximation to the binomial distribution, we first need to calculate the mean and standard deviation of the distribution.

Mean: 
μ = np = 100 * (1/5) = 20

Standard deviation: 
σ = √[npq] = √[(100)*(1/5)*(4/5)] = 4

Now we can use the formula for the z-score:

z = (X - μ) / σ 
z = (25 - 20) / 4 
z = 1.25

Therefore, the z-score corresponding to X = 25 is 1.25, which is answer choice C.

A Binomial Distribution Has P = 1/5 and Q =