Question

In a large population, about 10% of people do not like the taste of cilantro, an herb used in cooking. A researcher takes a random sample of 15 people and surveys whether they like cilantro. Use the binomial distribution to compute the probability that exactly 6 of the people in the sample do not like cilantro. Identify the following information required to find the probability of people who do not like the taste of cilantro.

Answer 1

0.0019390

Explanation:

10% of people do not like the taste of cilantro

A researcher takes a random sample of 15 people and surveys whether they like cilantro

Use the binomial distribution to compute the probability that exactly 6 of the people in the sample do not like cilantro.

Probability of success = 0.10 = p

Probability of failure = 0.9 =q

n = 15

r = 6

Formula :
`P(X=r)=^nC_rp^r q^(n-r)`

`P(X=6)=^(15)C_6 (0.1)^6 (0.9)^(15-6)`

`P(X=6)=(15!)/(6!(15-6)!) (0.1)^6 (0.9)^(15-6)`

`P(X=6)=0.0019390`

Hence the probability that exactly 6 of the people in the sample do not like cilantro is 0.0019390