A biologist estimates that 70% of the deer in a region carry a certain type of tick. For a sample of 300 deer selected at random, what is the chance that 216 or fewer deer have
This tick?
A) 0.794
B) 0.206
C) 0.864
D) 0.588

Question

Quizplus · Accepted Answer

This problem can be solved using the normal approximation to the binomial distribution. The mean (μ) of the distribution is n*p = 300*0.70 = 210, and the standard deviation (σ) is sqrt(n*p*(1-p)) = sqrt(300*0.70*0.30) ≈ 8.37. To find the probability of 216 or fewer deer having the tick, we calculate the z-score for 216, which is (216 - 210) / 8.37 ≈ 0.72. Looking up this z-score in a standard normal distribution table or using a calculator gives a probability of approximately 0.7642. However, due to the continuity correction (since we're approximating a discrete distribution with a continuous one), we adjust our value slightly, which can lead to the answer closest to 0.794. This approximation and the choices given suggest that the calculation or the interpretation of the z-score and continuity correction leads to the selection of choice A as the closest correct option.

A Biologist Estimates That 70% of the Deer in a Region