A biologist estimates that 60% of deer in the region carry a certain type of tick.For a sample of 300 deer selected at random, what is the chance that 186 or fewer deer have this tick?
A)0.8135
B)0.7782
C)0.7344
D)0.7290

Question

Quizplus · Accepted Answer

This problem requires us to use the binomial distribution to determine the probability of getting 186 or fewer deer with the tick out of a sample of 300 deer. We can use the formula P(X ≤ 186) = ΣP(X = k), where k = 0 to 186.

The probability of any individual deer having the tick is p = 0.6, and the probability of any individual deer not having the tick is q = 1-p = 0.4.

Using the binomial probability formula, we can calculate the probability of getting exactly k deer with the tick out of a sample of 300:

P(X = k) = (300 choose k) * 0.6^k * 0.4^(300-k)

Using a calculator or software, we can find the cumulative probabilities for k = 0 to 186 and sum them to get P(X ≤ 186):

P(X ≤ 186) = ΣP(X = k) from k=0 to 186

P(X ≤ 186) = 0.7782

Therefore, the answer is B: 0.7782.

A Biologist Estimates That 60% of Deer in the Region