Compute P(X) using the binomial probability formula. Then determine whether the normal distribution can be used to estimate this probability. If so, approximate P(X) using the normal distribution and compare the result with the exact probability. nequals=5353, pequals=0.30.3, and Xequals=20

Answer and Step-by-step explanation: P(X) calculated by the binomial probability formula is:

P(X) = .

P(20) =

P(20) =

P(20) = 0.0552

To determine whether the normal distribution can be used to estimate this probability, both n.p and n.(1-p) must be greater than 5:

n . p = 53*0.3 = 15.9

n.(1-p) = 53(1-0.3) = 37.1

Since both ARE greater than 5, normal distribution can be used.

To approximate:

mean = n . p = 15.9

standard deviation = = 3.34

Find the z-score:

z = =

z-score = 0.8907

Comparing values:

0.8907 - 0.0552 = 0.8355