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# Normal probability problems

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(1) The average number of humming birds per hour on a particular feeder is 5. Find the probability that exactly 3 humming birds feed during a particular hour using the correct table or formula.

(2) Weights for students applying to a Sumo wrestling school are normally distributed, with a mean of 250 pounds and a standard deviation of 25 pounds. To be eligible to enter, a person must weight in the top 15%. What is the lowest weight a student can have and still be eligible to enter the school.

(3) Determine the minimum required sample size if you want to be 95% confident that the sample mean is within 2 units of the true population mean. Assume that sigma = 7.8 is known and that the population is normally distributed.

(4) A horticulturalist wants to study the growth rate of a particular variety of Bougainvillea. From a sample of 16 randomly selected Bougainvilleas, the mean growth rate was 2.23 inches/week and the sample standard deviation was 0.77 inches/week. Find a 90% confidence interval for the mean growth rate of all Bougainvilleas.