Probability and Confidence Interval

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10.
Rabbits like to eat the cauliflowers in Mimi’s garden. There are 10 cauliflowers in her garden
which will be ready to harvest in about 10 days. Based on her experience, the probability of a
cauliflower being eaten by the rabbits before harvest is 0.40.
(a) Let X be the number of cauliflowers that Mimi harvests (that is, the number of
cauliflowers not eaten by rabbits). As we know, the distribution of X is a binomial
probability distribution. What is the number of trials (n), probability of successes (p) and
probability of failures (q), respectively?
(b) Find the probability that Mimi harvests at least 8 of the 10 cauliflowers. (round the
answer to 3 decimal places) Show all work. Just the answer, without supporting work,
will receive no credit.
11.
The heights of pecan trees are normally distributed with a mean of 10 feet and a standard
deviation of 2 feet. Show all work. Just the answer, without supporting work, will receive no
credit.
(a) What is the probability that a randomly selected pecan tree is between 7 and 11 feet
tall? (round the answer to 4 decimal places)
(b) Find the 40th percentile of the pecan tree height distribution. (round the answer to 2
decimal places)
13.
In a study designed to test the effectiveness of acupuncture for treating migraine, 100 patients
were randomly selected and treated with acupuncture. After one-month treatment, the number of
migraine attacks for the group had a mean of 2 and standard deviation of 1.5.
Construct a 95% confidence interval estimate of the mean number of migraine attacks for people
treated with acupuncture.
Show all work. Just the answer, without supporting work, will receive no credit.

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