Question

A biologist estimates that 40% of the deer in a region carry a certain type of tick. For a sample of 300 deer selected at random, what is the probability that fewer than 124 deer have this tick?

Answer 1

0.703

Explanation:

By inspection this is a binomial probability distribution problem.

We are given;

Probability that the deer in a region carries a certain type of tick; p = 40% = 0.4

Sample size; n = 300

Now we want to find the probability that fewer than 124 deer have this tick.

Thus is at P(x ≤ 124)

Formula for binomial distribution problem is;

P(X = x) = C(n, x) × p^(x) × (1 - p)^(n - x)

But now in this question,

P(x ≤ 124) = P(0) + P(1) + P(2) +.... P(124)

Getting all the Probabilities from P(0) to P(124) is too long we will make use of an online binomial probability distribution calculator with the result attached as an image.

In the calculator we input n = 300; p = 0.4; and P(X ≤ x)

We have a value of 0.703