MATH 3339 UPDATED SCRIPT 2026
PRACTICE SOLUTIONS GRADED A+
● binomial distribution. Answer: Fixed probability; given number of
trials; only 2 possible outcomes
● mean for binomial distribution. Answer: μ = np
● standard deviation for binomial distribution. Answer: σ = √(np(1-p))
● R command: For binomial distribution, n=50 and p=0.4, find P(X <=
5).. Answer: pbinom(5, 50, .4)
● R command: For binomial distribution, n=50 and p=0.4, find P(X =
5).. Answer: dbinom(5, 50, .4)
● hypergeometric distribution. Answer: from two types of items (A and
B); select some fixed number; count how many of A you get
● R command: For hypergeometric distribution, m=20, n=15, and k=5,
find P(X <= 1).
m = things counted
n = not counted
, k = amount selected. Answer: phyper(1, 20, 15, 5)
phyper(x, m, n, k)
● hypergeometric formula for P(X=x).. Answer: P(X=x) = C(m, x) *C(n,
k-x) / C(m+n, k)
● R command: get LSRL equation. Answer: lm(y~x)
● interpret coefficient of determination. Answer: ##% of the variation in
y is explained by the LSRL and x
● poisson distribution. Answer: Probability distribution for the number
of arrivals during each time period
● R command: poisson distribution, mean=2.8, find P(X <=1).. Answer:
ppois(1, 2.8)
● percentile. Answer: A point on a ranking scale of 0 to 100. The 50th
percentile is the midpoint; half the people in the population being
studied rank higher and half rank lower.
● in a collection of 30 data measurements, which measurement
represents the 25th percentile?. Answer: n = 30
P = 0.25
PRACTICE SOLUTIONS GRADED A+
● binomial distribution. Answer: Fixed probability; given number of
trials; only 2 possible outcomes
● mean for binomial distribution. Answer: μ = np
● standard deviation for binomial distribution. Answer: σ = √(np(1-p))
● R command: For binomial distribution, n=50 and p=0.4, find P(X <=
5).. Answer: pbinom(5, 50, .4)
● R command: For binomial distribution, n=50 and p=0.4, find P(X =
5).. Answer: dbinom(5, 50, .4)
● hypergeometric distribution. Answer: from two types of items (A and
B); select some fixed number; count how many of A you get
● R command: For hypergeometric distribution, m=20, n=15, and k=5,
find P(X <= 1).
m = things counted
n = not counted
, k = amount selected. Answer: phyper(1, 20, 15, 5)
phyper(x, m, n, k)
● hypergeometric formula for P(X=x).. Answer: P(X=x) = C(m, x) *C(n,
k-x) / C(m+n, k)
● R command: get LSRL equation. Answer: lm(y~x)
● interpret coefficient of determination. Answer: ##% of the variation in
y is explained by the LSRL and x
● poisson distribution. Answer: Probability distribution for the number
of arrivals during each time period
● R command: poisson distribution, mean=2.8, find P(X <=1).. Answer:
ppois(1, 2.8)
● percentile. Answer: A point on a ranking scale of 0 to 100. The 50th
percentile is the midpoint; half the people in the population being
studied rank higher and half rank lower.
● in a collection of 30 data measurements, which measurement
represents the 25th percentile?. Answer: n = 30
P = 0.25
