Statistics Problem Set: Binomial Random Variables
38. Suppose x is a binomial random variable with n = 3 and p
= 3
a. calculate the value of p(x), x = 0,1,2,3 using the
formula for a binomial probability distribution
b. using your answers to part a, give the probability
distribution for x in tabular form
42. The binomial probability distribution is a family of
probability distributions with each single distribution depending on the values
of n and p. Assume that x is a binomial random variable with n =4.
a. determine a value of p such that the probability
distribution of x is symmetric
b. determine a value of p such that the probability
distribution of x is skewed to the right
c. determine a value of p such that the probability
distribution of x is skewed to the left
d. graph each of the binomial distributions you obtained in
parts a, b, c. locate the mean for each distribution on its graph.
e. in general for what values of p will a binomial
distribution be symmetric? skewed to the right? skewed to the left?
80. find the are under the standard normal probability
distribution between the following pairs of z-scores:
a. z=0 and z=2.00
b. z=0 and z=3
c. z=0 and z=1.5
d. z=0 and z=.80
82. find the following probabilities for the standard normal
random variable z:
a. P(-1<z<1)
b. P(-2<z<2)
c. P(-2.16< or =z < or = .55)
d. P(-.42<z<1.96)
e. P(z< or = 2.33)
f. P(z<2.33).
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