MATH 3339 EXAM 1 | QUESTIONS AND ANSWERS | 2026 UPDATE | WITH COMPLETE
SOLUTIONS.
Chebyshev's Inequality - (answer)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 - (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
, MATH 3339 EXAM 1 | QUESTIONS AND ANSWERS | 2026 UPDATE | WITH COMPLETE
SOLUTIONS.
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
rank = nP+0.5 = 8
8th measurement = 25th percentile
find which number is at a certain percentile - (answer)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
2b) if decimal of rank = 0.5, take average. EX: if 10th %-tile = 19.5 -> get average of 19th and 20th
element.
R command: 5 number summary - (answer)fivenum(listname)
R command: find value of 95th percentile in list - (answer)quantile(listname, 0.95)
R command: stem plot - (answer)stem(listname, scale=(optional # from 0 to 1))
population variance formula - (answer)
sample variance formula - (answer)R command: sd()
coefficient of variation formula - (answer)greater cv -> greater variability
SOLUTIONS.
Chebyshev's Inequality - (answer)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 - (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
, MATH 3339 EXAM 1 | QUESTIONS AND ANSWERS | 2026 UPDATE | WITH COMPLETE
SOLUTIONS.
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
rank = nP+0.5 = 8
8th measurement = 25th percentile
find which number is at a certain percentile - (answer)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
2b) if decimal of rank = 0.5, take average. EX: if 10th %-tile = 19.5 -> get average of 19th and 20th
element.
R command: 5 number summary - (answer)fivenum(listname)
R command: find value of 95th percentile in list - (answer)quantile(listname, 0.95)
R command: stem plot - (answer)stem(listname, scale=(optional # from 0 to 1))
population variance formula - (answer)
sample variance formula - (answer)R command: sd()
coefficient of variation formula - (answer)greater cv -> greater variability
