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1. Suppose 22% of a population consists of people with blonde hair. 6 people are randomly selected from this population.
Find the probability that exactly 2 of them have blonde hair.
Find the probability that at least 1 of them have blonde hair.
2. Suppose 22% of a population consists of people with blonde hair. 1000 people are randomly selected from this population. Find the probability that at least 224 of them have blonde hair. [When solving this by hand, use the normal approximation to the binomial distribution… don’t forget the continuity correction factor!]
3. The times of the finishers in the New York City 10 km run are normally distributed with mean 61 minutes and standard deviation 9.3 minutes.
Find the probability that a randomly selected finisher does the race in under 55 minutes.
Find the probability that a randomly selected finisher completes the race in between 62 and 85 minutes.
Find the 30th percentile.
If 16 different runners are randomly selected, find the probability that their mean finishing time is under 55 minutes.
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