Final answer:
To find the probability of at least 34 sea gull sightings in a random sample of 50 bird sightings, we can use the binomial probability formula and calculate the probabilities for 34 to 50 sea gull sightings and sum them up.
Step-by-step explanation:
To find the probability that in a random sample of 50 bird sightings at least 34 are sea gulls, we can use the binomial probability formula.
The formula for the probability of getting exactly x successes in n trials, where the probability of success in each trial is p, is:
P(x) = (nCx) * p^x * (1-p)^(n-x)
To find the probability of at least 34 sea gull sightings, we need to calculate the probabilities for 34, 35, 36, ..., 50 sea gull sightings and sum them up.
The probability that in a random sample of 50 bird sightings at least 34 are sea gulls is approximately 0.994 (rounded), which corresponds to option a).