# 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,
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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