I need to submit before May 16. Please do it correctly. and I need the process of the answers. thanks.
Name: Section #:
6 – Assignment #1 — Due Saturday, May 16 11:
0am, 2020 Convert your
solution to one Word or PDF file and Submit it to D2L
For full marks you must clearly explain your answers, you will not receive any marks if only
1. A large set of data is found to be bell-shaped. According to the Empirical rule, approximately
99.7% of the population (from which the data was taken) lies in the interval (60, 132). What
must have been the standard deviation of the data?
2. Consider the following probability distribution for X:
x 0 1 2 3
f(x) .1 .3 .25 .35
Calculate E(2X + 1).
3. Consider the random variable X with cumulative distribution function given below. What is
the probability X is an even number given that X is less than
x 2 3 4 5 6
F(x) .25 .5 .6 .8 1.0
Questions 4 and 5 refer to the following setup. A sample of 200 married men over the
age of 50 were classified according to their education and number of children:
0-1 children 2-3 children Over 3 children
High school 14 37 32
Bachelors degree 19 42 17
Graduate degree 12 17 10
4. If one person is chosen at random from the sample, let E be the event that the chosen person
has over 3 children, and let F be the event that the chosen person has a university degree
(either bachelors or graduate). Determine which of the following statements are true and
(i) P (F|E) = 27
(ii) Events E and F are mutually exclusive.
(iii) Events E and F are independent.
5. Suppose 3 people are chosen at random from the sample. Find the probability that exactly
two have a high school education (ie. no university degree).
6. For a particular experiment, if X and Y are independent events with P (X) = .7 and P (Y ) =
.6, what is the probability that X or Y occurs?
7. Celina is an executive who receives an average of 8 phone calls each afternoon between 2 and
4. Assuming that the calls are Poisson distributed, what is the probability that Celina will
receive three or more calls between 2:30 and 3:30?
8. After researching tumors of a particular type, a doctor learns that out of 10, 000 such tumors
examined, 1500 are malignant and 8500 are benign. A diagnostic test is available which gives
the correct diagnosis 80% of the time (whether the tumor is malignant or not). The doctor
has discovered the same type of tumor in a new patient and decides to begin diagnosis by
using the diagnostic test. If the test says that the tumor is malignant, what is the probability
that the patient actually does have a malignant tumor?
9. If X and Y are independent events with P (X) = 0.5 and P (XandY ) = 0.35, calculate P (Y ).
10. Suppose that the probability of a bank making a mistake in processing a deposit is .002.
(a) If 5,000 deposits are audited, what is the probability that the number of mistakes that
were made was no more than one? Calculate this probability directly, without using a
(b) If it is appropriate to do so, use a Poisson approximation to calculate the same probability
you calculated in part (a). If it is not approriate to do so, explain why not.