A student dance committee is to be formed consisting of 2 boys and 3 girls. If the membership is to be chosen from 4 boys and 8 girls, how many different committees are possible?
Step 11 of 3
For committees, order is not important (being the first member of the committee has no special meaning).
We are dealing with combinations.
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The most famous geyser in the world, Old Faithful in Yellowstone National Park, has a mean time between eruptions of 85 minutes. If the interval of time between eruptions is normally distributed with standard deviation 21.25 minutes, answer the following questions: (a) What is the probability that a randomly selected time interval between eruptions is longer than 95 minutes? (b) What is the probability that a random sample of 20 time intervals between eruptions has a mean longer than 95 minutes? (c) What is the probability that a random sample of 30 time intervals between eruptions has a mean longer than 95 minutes? (d) What effect does increasing the sample size have on the probability? Provide an explanation for this result. (e) What might you conclude if a random sample of 30 time intervals between eruptions has a mean longer than 95 minutes? (f) On a certain day, suppose there are 22 time intervals for Old Faithful. Treating these 22 eruptions as a random sample, the likelihood the mean length of time between eruptions exceeds ____ minutes is 0.20.