Question

**Suppose the probability that Joe Schmo makes a single
free throw is .37, and suppose he shoots n = 12 free throws in a
particular game. Let Y denote the number of made free
throws.**

**a. The distribution of Y is:**

**A. skewed negatively B. not skewed C. skewed
positively**

**b. Use the binomial formula to compute the probability
that Joe Schmo will make exactly 3 free throws. (5
decimals)**

** **

**c. What are the least and most likely number of free
throws made by Joe Schmo?**

**d. What is the exact binomial probability that Joe Schmo
makes at least half of his free throws? (4 decimals)**

**e. Show that the mean and variance of Y are 4.44 and
2.7972, respectively.**

**f. What is the normal approximation (with continuity
correction) to the exact probability of Part 2 above? (5
decimals)**

**g. Determine whether the “guidelines” for assessing
whether the sample size is “sufficiently large” for a “good normal
approximation” are satisfied or not.**

Answer #1

(Since there are more than 4 parts i will answer first 4 parts)

probability distribution in binomial :

the binomial plot for p =0.37 and n=12 is :

a.

we can see probability is more in right side so it is
**positively skewed**

b.

P(3) = 12C3 * (0.37^3) * (1-0.37)^(12-3)

**P(3) = 0.1742**

c.

as we can see in the plot of probability :

**least likely = 12**

**most likely = 4**

d.

P(atleast half) = P(x>=6) = P(6)+P(7)+P(8)+.....+P(12)

**P(atleast half) = 0.2588**

**P.S. (please upvote if
you find the answer satisfactory)**

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