Question

A biologist estimates that 40% of deer in the region carry a certain type of tick. for a sample of 300 deer selectetd at random, what is the chance that 124 or fewer deer have this tick?

Answer 1

Let x be a discrete binomial random variable that measures the number of successes in n trials.
Let p = 0.4 be the probability of success, that is, the probability that a deer has the aforementioned type of tick.
So the probability that 124 deer or less have this type of tick is calculated using the probability formula for a binomial distribution.
P (X <= x) = sum from x = 0 to x = 124 of (300! / ((X! * (300-x)!)) * (P ^ x) * (1-p) ^ n-x.
Finally the probability is 0.7030
Below is an image with the formula used and the result