Question

Determine the indicated probability for the binomial distribution. Then find the mean and standard deviation. Round the standard deviation to the nearest thousandth.

n=8 p =.2

P( Fewer than 3)

Mean=

Standard Deviation =

Answer 1

Solution :

Given that,

p = 0.2

q = 1 - p = 1 - 0.2 = 0.8

n = 8

Using binomial distribution,

mean = n * p = 8 * 0.2 = 1.6

standard deviation = n * p * q = 8 * 0.2 * 0.8 = 1.28 = 1.131

Using binomial probability formula ,

P(X = x) = ((n! / x! (n - x)!) * p^x * (1 - p)^{n - x}

P(X < 3) = P(x = 0) + P(x = 1) + P(x = 2)

=  ((8! / 0! (8)!) * 0.2⁰ * (0.8)⁸ +   ((8! / 1! (7)!) * 0.2¹ * (0.8)⁷ +  ((8! / 2! (6)!) * 0.2² * (0.8)⁶

= 0.1678 + 0.3355 + 0.2936

P(X < 3) = 0.7969

Probability = 0.7969