Question

a) 30% of people in a city smoke. If 7 individuals are randomly selected what is the probability that exactly 4 smoke?

b) Let X be a binomial distribution with n = 30 and p = .6 then the standard deviation is

c) Compute the probability of X successes.
   n = 7, X = 6, p = 0.3

Answer 1

Solution :

a ) Given that ,

p = 0.30

1 - p = 1 -0.30 = 0.70

n = 7

x = 4

Using binomial probability formula ,

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

P(X = 4) = ((7! / (7 - 4)!) * 0.30⁴ * 0.70^{7 - 4}

= 0.0972

Probability = 0.0972

b ) Given that ,

p = 0.60

q = 1 - p = 1 - 0.60 = 0.40

n = 30

Using binomial probability formula ,

=  n * p * q

= 30* 0.60 * 0.40

= 7.2

= 2.6833

The standard deviation is = 2.6833

c ) Given that ,

p = 0.30

1 - p = 1 -0.30 = 0.70

n = 7

x = 6

Using binomial probability formula ,

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

P(X = 6) = ((7! / (7 - 6)!) * 0.30⁶ * 0.70^{7 - 6}

= 0.0036

Probability = 0.0036