Question

Suppose that 1/5 of all pet owners have their pets bathed professionally. If 10
pet owners are selected at random, what is the probability exactly 3 have their pets bathed
professionally? (Hint: What kind of distribution is this?)

(b) If 10 pet owners are selected, what is the mean and standard deviation of the
number of pet owners have their pets bathed professionally?

Answer 1

Solution

Given that ,

p = 0.2

1 - p = 0.8

n = 10

(a)

Using binomial probability formula ,

P(X = x) = (_n C _x) * p^x * (1 - p)^{n - x}

P(X = 3) = (₁₀ C ₃) * 0.2³ * (0.8)⁷

= 0.2013

Probability = 0.2013

(b)

Mean = = n * p = 10 * 0.2 = 2

Standard deviation = = n * p * q = 10 * 0.2 * 0.8 = 1.265