Download REVIEWING CHAPTERS-5- 6

REVIEWING CHAPTER 6 – There are two major problem types:
(1) Finding probabilities in a normal distribution
(2) Finding scores in a normal distribution
HERE IS A PROBLEM that asks for ALL you need to know from chapter 6:
For women in the United States the overall mean height is µ = 63.7 inches with a standard
deviation of σ = 2.7 inches. For men in the US, the overall height is µ = 69.1 inches and a
standard deviation of σ = 2.9 inches. Both distributions are normally distributed.
Answer the following questions. Show all steps in your work, no matter how small for full
credit.
(a) What is your height in inches? _____________
(b) Use the mean and standard deviation of your gender to sketch the graph of the normal
curve. Label the mean and one, two and three standard deviations to the left and right of
the mean
(c) Place your height in the graph. Use formulas to answer: how many standard deviations
are you from the mean for your gender?
(d) Considering that any observation that is more than two standard deviations from the
mean is unusual, is yours an unusual height?
(e) What percentile is your height in the distribution of your gender?
(f) What is the probability that a person of your gender selected at random is taller than you?
(g) What height will place a person of your gender in the 96th percentile?
(h) Show the calculator input that answers question (e)
(i) Show the calculator input that answers question (f)
(j) Show the calculator input that answers question (g)
CHAPTER 5 – EXPERIMENTAL PROBABILITIES
(k) SIMULATE selecting at random someone from your gender: randNorm(mean,standard
devation) (this is in the MATH, PRB). Do it 20 times and each time record the height
obtained (3 decimal places).
(l) Use those results to find the experimental probability of selecting a person who is taller
than you. (# of times you got someone taller than you / 20)
(m) How does the experimental probability from part (l) compare to the theoretical
probability from part (f)?
(n) Comment on the Law of Large Numbers in reference to this context.