Hofstra University Statistical Integer Distribution Types Report

1.Using Microsoft Excel, plot the following distributions using the functional form. DO NOT USE BUILT IN DISTRIBUTION FUNCTIONS IN EXCEL (BINOM.DIST, POISSON.DIST, NORM.DIST). You may use factorial and exponential built in functions. To show your work, attach the spreadsheet you used.

a.Binomial distribution

i.n = 30, p = 0.5, 0 ≤ x ≤ 30 in integer steps

ii.n = 50, p = 0.7, 0 ≤ x ≤ 50 in integer steps

b.Poisson distribution:

i.μ = 10.5, 0 ≤ x ≤ 30 in integer steps

ii.μ = 17.5, 0 ≤ x ≤ 30 in integer steps

c.Normal distribution

i.-5 ≤ x ≤ 5 in 0.1 steps, μ = 0, σ = 1

ii.-5 ≤ x ≤ 5 in 0.1 steps, μ = 0, σ = 0.5

iii.-5 ≤ x ≤ 5 in 0.1 steps, μ = 1, σ = 1.5

2.In the x-ray detector example from the class, the coefficient of variation was 0.01 with 10,000 photons. How many photons per minute would be required to reduce the coefficient of variation to 0.005?

3.In the attached spreadsheet “CLT_data.xlsx,” you will find data that was pulled from a uniform distribution between -1 and 1 (equal probability of any value between -1 and 1). Demonstrate how the central limit theorem can convert non-normal data to normal data. Show your work by attaching the spreadsheet and embed relevant graphs in the word document!

4.In the attached spreadsheet “avg_data.xlsx,” plot the measurements in a histogram. Calculate the mean, median, variance, standard deviation, standard error of the mean, and coefficient of variation. You may use built in functions for mean and standard deviation only.

5. You are playing Dungeons and Dragons (D&D) and your party is in deep trouble. You have come upon a very powerful demon who has mortally wounded all your teammates. You are the last one standing. In D&D, you roll a twenty-sided die to determine if you hit the target. If you roll a 20 (so called “natural 20”), your damage is doubled. You estimate that you have 3 chances to strike the demon before it kills you and that you will need at least 1 natural 20 to slay the demon and save the realm. What is the probability that you will roll a natural 20 in one of those three rolls?