Question

# Compute the probability of 6 successes in a random sample of size n=11 obtained from a...

Compute the probability of 6 successes in a random sample of size n=11 obtained from a population of size N=70 that contains 25 successes.

The probability of 6 success is?

Binomial Probability Distribution: For a random variable X, given the probability of success is p, and probability of failure is q = (1-p), the probability of obtaining x successes in n independent trials of a binomial experiment, is

The probability of 6 successes in a random sample of size n=11 obtained from a population of size N=70 that contains 25 successes is

Here,

Sample size n=11,

No. of successes r = 6,

Probability of success p = (No of successes)/ Population size = 25/70 = 0.36

Probability of failure q = 1-p = 1- 0.36 = 0.64

Thus, probability of 6 successes is

= 0.1079 = 0.11

The probability of 6 successes in a random sample of size n=11 obtained from a population of size N=70 that contains 25 successes is 0.11.

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