Question

Consider the following binomial experiment: A survey shows 69 % of households in Centercity own a DVD player. In a random sample of 13 households in this city, what is the probability that exactly 6 households own a DVD player?

a) 0.0506
b) 0.0507
c) 0.0509
d) 0.0505
e) 0.0511
f) None of the above,

Answer 1

The probability that exactly 6 households own a DVD player is 0.0509. Hence the correct option is c.

Identify parameters:

p = probability of owning a DVD player = 0.69

n = sample size = 13

k = desired number of successes (owning DVD player) = 6

Use the binomial probability mass function:

P(k successes in n trials) = (n choose k) * p^k * (1-p)^(n-k)

Calculate the probability:

P(6 successes in 13 trials) = (13 choose 6) * 0.69^6 * (1-0.69)^(13-6)

≈ 0.0509

Therefore, the probability that exactly 6 households own a DVD player is approximately 0.0509. Hence the correct option is c.