1. For the following series of observations find the mean, median, and midrange.
6, 5, 2, 11, 5, 3, 9, 13, 20, 5, 16, 1.
2. Suppose your instructor assigns grade for the course based on your performance as following: 35% for quizzes, 25% for midterm exam, 35% for final exam, and 5% for attendance and class participation. What would your grade score be if you scored 75 points on quizzes, 80 points on midterm exam, 85 points on your final exam, and 90 points on attendance and class participation? (Calculate mean value from the following probability table). Round your answer to the nearest integer.
Quizzes Midterm Exam Final Exam Attendance
Scores, X 75 80 85 90
Probability, P(X) 0.35 0.25 0.35 0.05
μ =
– 2 –
Use Binomial Distribution to solve problems 3 – 4
3. Over a long period of time a certain drug has been effective in 80% of the cases in which it has been prescribed. If a doctor is now administering this drug to five patients, what is the probability that it will be effective for
a) one patient
P(X = 1) =
b) less than two patients
P(X < 2) =
4. If 40% of employees in the company are females and 6 employees are randomly chosen to serve on a committee, what is the probability that:
a) No women will be selected
P(X=0) =
b) One or more women will be selected
P(X ≥ 2)
Use Poisson Distribution to solve problem 5
5. The expected number of typographical errors on a page of a certain magazine is 2.75
What is the probability that the next page you read contains more than 1 typographical error:
P(X >1) =
– 3 –
Use Normal Distribution to solve problems 6–8
6. If Z is a standard normal variable find the probabilities of:
a) P(Z < −1.68) =
b) P(−1.68< Z < 1.89) =
c) P(Z > 1.89) =
7. It is said that sufferers of a cold virus experience symptoms for 7 days. However, the amount of time is a normally distributed random variable whose mean is 7.5 days and whose standard deviation is 1.2 days.
What proportion of cold sufferers experiences symptoms for between 7 and 10 days?
P(7 < X < 10 ) =
8. The weekly salaries of teachers in one state are normally distributed with a mean of $1850 and a standard deviation of $75. What is the amount of money that separates
a) bottom 3% of these teachers
b) top 14% of these teachers
