MATH 3339 TEST 1 REVIEW EXAM
QUESTIONS AND ANSWERS 2026
VERIFIED.
Chebyshev's Inequality - ANS The percentage of the observations that lie within k
standard deviations of the mean is at least 1 - (1/k^2) when k > 1
binomial distribution - ANS Fixed probability; given number of trials; only 2 possible
outcomes
mean for binomial distribution - ANS μ = np
standard deviation for binomial distribution - ANS σ = √(np(1-p))
R command: For binomial distribution, n=50 and p=0.4, find P(X <= 5). - ANS pbinom(5,
50, .4)
R command: For binomial distribution, n=50 and p=0.4, find P(X = 5). - ANS dbinom(5, 50,
.4)
hypergeometric distribution - ANS 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).
1
, m = things counted
n = not counted
k = amount selected - ANS phyper(1, 20, 15, 5)
phyper(x, m, n, k)
hypergeometric formula for P(X=x). - ANS P(X=x) = C(m, x) *C(n, k-x) / C(m+n, k)
R command: get LSRL equation - ANS lm(y~x)
interpret coefficient of determination - ANS ##% of the variation in y is explained by the
LSRL and x
poisson distribution - ANS Probability distribution for the number of arrivals during each
time period
R command: poisson distribution, mean=2.8, find P(X <=1). - ANS ppois(1, 2.8)
percentile - ANS 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? -
ANS n = 30
P = 0.25
rank = nP+0.5 = 8
8th measurement = 25th percentile
find which number is at a certain percentile - ANS 1) %-tile = nP+0.5
2a) if decimal of %-tile != 0.5, choose round rank. EX: if 10th %-tile = 19.25 -> 19th element is
10th percentile
2
QUESTIONS AND ANSWERS 2026
VERIFIED.
Chebyshev's Inequality - ANS The percentage of the observations that lie within k
standard deviations of the mean is at least 1 - (1/k^2) when k > 1
binomial distribution - ANS Fixed probability; given number of trials; only 2 possible
outcomes
mean for binomial distribution - ANS μ = np
standard deviation for binomial distribution - ANS σ = √(np(1-p))
R command: For binomial distribution, n=50 and p=0.4, find P(X <= 5). - ANS pbinom(5,
50, .4)
R command: For binomial distribution, n=50 and p=0.4, find P(X = 5). - ANS dbinom(5, 50,
.4)
hypergeometric distribution - ANS 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).
1
, m = things counted
n = not counted
k = amount selected - ANS phyper(1, 20, 15, 5)
phyper(x, m, n, k)
hypergeometric formula for P(X=x). - ANS P(X=x) = C(m, x) *C(n, k-x) / C(m+n, k)
R command: get LSRL equation - ANS lm(y~x)
interpret coefficient of determination - ANS ##% of the variation in y is explained by the
LSRL and x
poisson distribution - ANS Probability distribution for the number of arrivals during each
time period
R command: poisson distribution, mean=2.8, find P(X <=1). - ANS ppois(1, 2.8)
percentile - ANS 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? -
ANS n = 30
P = 0.25
rank = nP+0.5 = 8
8th measurement = 25th percentile
find which number is at a certain percentile - ANS 1) %-tile = nP+0.5
2a) if decimal of %-tile != 0.5, choose round rank. EX: if 10th %-tile = 19.25 -> 19th element is
10th percentile
2
