Statistics and Probability Problem Set
1. What is the mean, median, mode, and standard deviation for the following 13 items:
2. There are two types of university entrance exams in US: SAT and ACT. Both of them are
standardized test. Midwestern schools use ACT for admission, rather than the SAT. You got a debate
with your friends which school has better undergraduates. One way to compare the quality of students is
to compare standardized test scores. Unfortunately, School A, like many Midwestern schools, uses the
ACT for admission, rather than the SAT, the test of choice for School B. The ACT has a top score of 36
and SAT scores can be converted into ACT scores using the equation ACT = -3.4 + 0.02339(SAT).
School Bís entering freshman class has a mean SAT score of 1230 and a standard deviation of 240.
School A has a mean ACT of 26.9 and a standard deviation of 5.4. Convert school Bís mean and standard
deviation of SAT scores to ACT scale.
3. It takes five people working on different tasks to produce a new product. A small workplace has five
different workers and the plant manager wants to experimentally compare which workers/job
combinations produce the product in the fastest time. If they wanted to perform this experiment, how
many different combinations must they analyze?
4. Dominoís Pizza offers pizzas with two different sizes, three different types of crusts and up to 10
toppings. For topping you have a choice of having or not having.
How many different types of pizzas can be made?
5.To win the Texas Two-Step lotto game, players must match 4 lotto balls, drawn from 1-35 and a bonus
ball, drawn from another pool of numbers, also numbered 1-35. What is the probability that numbers
drawn at random will match the winning numbers?
6. An economics exam has 10 questions. The student must answer 3 of the first 4 and 2 of the last 6. How
many different sets of questions can a student elect to answer?
7. A 25 member sorority must choose its three officers: president, vice president and treasurer. How many
different slates of officers (president, vice president, treasurer) are possible in this sorority?
8. According to the 2000 Census 15.1% of Maryland residents live in Prince Georgeís (PG) county, 27.9%
of Maryland residents are African American, and 9.5% of Maryland are both PG County residents and
A) What fraction of the population that is either a PG county resident or African American?
B) What fraction of the population that is either a PG county resident or non-African American?
C) What is the fraction of the population that is a non-PG county resident and African American?
9. A college senior has applied for admission to two medical schools, A and B. She estimates the
probability of acceptance at A at 0.7 and the probability of acceptance at B at 0.4 and the probability that
she will be admitted to both at 0.2. What is the chance she will not be accepted at either school?