Probability questions on NBA.
ONLY DO PROBLEM 1 and 2 from the four questions in the document.
Problem 1 ? Consider the NBA Data Set Given:
A. What proportion of these players are less than 74 inches tall?
B. Suppose a random sample of 25 of these players is taken and x is the number of players in the sample who are less than 74 inches tall. Find P(x=0), P(x=1), P(x=2), P(x=3), P(x=4), P(x=5).
C. Note that x in part b has a binomial distribution with lambda=np. Use the Poisson probabilities table to approximate P(x=0), P(x=1), P(x=2), P(x=3), P(x=4), P(x=5).
D. Are the probability distributions of parts b and c consistent or is the Poisson approximation inaccurate. Explain.
Problem 2 ? Consider the Data on Heights of NBA Players in the Data Set Given:
A. Use Excel to obtain a histogram. Do these heights appear to be symmetrically distributed? If not, which direction do they seem to be skewed?
B. Compute mu and sigma.
C. What percentage of these heights lie in the interval mu - sigma to mu + sigma? What about in the interval mu - 2 sigma to mu + 2 sigma? In the interval mu - 3 sigma to mu + 3 sigma?
D. How do the percentages in part c compare to the corresponding percentages for a normal distribution (68%, 95%, and 99.7% respectively)?
This solution has an applied problem regarding NBA players and their heights.