______ANSWERS______
NAME
ISDS 361A
John Lawrence
Sample Exam #1
Open notes, book, etc.
A. (20)______
B. (15)______
C. (10)______
D. (10)______
E. (5)______
F. (15)______
G. (5)______
H. (5)______
I. (20)______
TOTAL (105) ______
A SCORE OF 100 WILL BE CONSIDERED PERFECT!
(A) The starting salaries of the first full-time job of last year’sCSUF business graduates are normally distributed with a mean of $34,500 and a standard deviation of $2,500.
1. What is the probability abusiness graduate last year had a starting salary of exactly $33,832.15?
The probability a continuous random variable = anyspecific number is 0.
2. What is the probability a business graduate last year had a starting salary between $30,000 and 35,000?
EXCEL:
=NORMDIST(35000,34500,2500,TRUE)-NORMDIST(30000,34500,2500,TRUE)_ = .543329
HAND:
3. What is the probability a business graduate last year had a starting salary greater than $31,650?
EXCEL: =1-NORMDIST(31650,34500,2500,TRUE) = .872857
HAND:
4. 90% of all of last year’s CSUF business graduates made at least how much?
EXCEL: =NORMINV(.10,34500,2500)= $31,296.12
(B) A random sample of 5 students in ISDS361A were asked, "How many hours per week do you work?" The responses: 0, 15, 40, 25, 40.
5.What is your best estimate for the average number of hours worked by all students inISDS361A? Give symbol and show work.
6.What is your best estimate for the standard deviation of the number of hours worked by all students in ISDS361A? Give symbol and show work. _s_= 17.103_
7.For this sample, what is the median? __25___ the mode? ___40___
(C ) An accounting graduate has a probability of .2 of staying more than 5 years with the firm that hired him upon graduation from college.
8.In a sample of 25 accounting graduates, what is the probability that 5 years from now exactly 6 are with the firm that hired them?
=BINOMDIST(6,25,.2,FALSE)= .163346
From table for n = 25, column p = .20, P(X 6) = .780, P(X 5) = .617 .780 - .617 = .163
9.In a sample of 15 accounting graduates, what is the probability that 5 years from now, between 2 and 5 are with the firm that hired them?
=BINOMDIST(5,15,0.2,TRUE)-BINOMDIST(1,15,0.2,TRUE) =.771823
P(2 X 5) = P(X 5) - P(X 1)
From table for n = 15, column p = .20, P(X 5) = .939, P(X 1) = .167 .939 - .167 = .772
(D)Of those that stay 5 years or less, the length of employment with the firm that hired them can be expressed by the following probability distribution, where
X = the number of years the employee stayed with the firm:
(10) Of all graduates that stay with the firm that hired them less than 5 years, what is the mean number of years they remain with the firm?
= E(X) = 1(.45) +2(.30) + 3(.10) + 4(.10) + 5(.05) = 2
(11)Of all graduates that stay with the firm that hired them less than 5 years, what is the standard deviation of the number of years they remain with the firm?
2 = [(12 )(.45) + (22 )(.30) + (32 )(.10) + (42 )(.10) + (52 )(.05)] - 22 = 1.40
____ .
= 1.40 = 1.183
(E-12)The average number of arrivals to the Titan Bookstore is 2 per minute. It is observed that: (1) no two arrivals occur simultaneously; (2) the probability distribution for the number of arrivals in a time period remains constant; and, (3) the time to the next arrival is independent of when the previous arrival occurred. What is the probability that in a 3-minute period, there are between 5 and 7 arrivals to the Titan Bookstore?
=POISSON(7,6,TRUE)-POISSON(4,6,TRUE) = .458923
Assumptions make this Poisson. If the average in 1 minute = 2, the average in 3 minutes is = 3(2) = 6. So we use the column for = 6.0 in the Poisson table.
P(5 X 7) = P(X 7) - P(X 4) = .744 - .285 = .459
(F)A student must get a "C" or better in ISDS361A to take Finance 320. The following is the joint probability distribution of the grades received for the final time in ISDS361A and the first time in FINANCE 320.
FINANCE 320
A B C D F
(FA)(FB)(FC)(FD)(FF)
A (IA) .06 .08 .04 .02 0
ISDS 361AB (IB) .06 .12 .08 .03 .01
C (IC) .03 .10 .28 .05 .04
(13)Bob is taking Finance 320. What is the probability he will get a "B" in the course? .30
Show work:
P(FB) = .08 + .12 + .10 = .30
(14)Jill got an "A" in ISDS 361A. What is the probability she will get an "A" in Finance 320? .30
Show work.
P(FA|IA) = P(FA and IA)/P(IA) = .06/.20 = .30
(15)Are getting a "C" in ISDS 361A and a "D" in Finance 320 a pair of independent events? YES
Show work.
Does P(IC and FD) = P(IC)P(FD)?
P(IC and FD) = .05 (from table)
P(IC)P(FD) = (.50)(.10) = .05
They are =; thus these events are independent!
(G-16)The probability density function of the length of time it takes a student to finish a one-hour Marketing 351 exam can be expressed as follows:
f(x) = 4x3for x between 0 and 1 hour
= 0for all other values of x
What is the probability it will take a randomly selected student between 48 minutes
(.8 hr.) and 54 minutes (.9 hr.) to complete a one-hour Marketing 351 exam? __.2465___ Show work:
(H-17)The following is the distribution of the ages of my students in a recent ISDS 361B class. Roughly sketch the cumulative relative frequency ogive.
Age Number
20-2510
25-3016
30-35 8
35-40 4
40-45 2
(I) Circle TRUE/FALSE
I-1TFThe population variance is the average of the squared deviations each value of x is from .
I-2.TFThe expected value of any expression is the weighted average of the possible values of the expression, weighted by the probabilities the expression will achieve each of these values.
I-3TFThe probability it will rain tomorrow is an example of the relative frequency approach to probability. Subjective Approach
I-4TFTo know the precise values of and for a population, each member of the population would have to be surveyed.
I-5TFIf the number of arrivals to a store follows a Poisson distribution with the average number of arrivals per hour = 3, the time between arrivals follows an exponential distribution with the average time between arrivals being 1/3 hour.
I-6TFStandard deviation is typically preferred to variance as a measure of variability because it is measured in the same units as the experimental unit.
I-7T FThe probability you pass Econ 310 is .8. If you fail Econ 310 the second time you take it you have a probability of .7 of passing it the second time. The probability you pass Econ 310 in one of the first two tires is .87. HINT: Use probability trees. Prob. = .94
I-8TFIf X = the starting salary of a male graduate and Y = the starting salary of a female graduate (salaries in $1000's), then P(X-Y > 0) is the probability a randomly selected male graduate will have a higher starting salary than a randomly selected female graduate.
I-9TFIn question I-8, (in $1000's) the average starting salary of male graduates is 30 with a standard deviation of 3 and for female graduates it is 29 with a standard deviation of 2. Then the average difference in starting salaries between a randomly selected male and female graduate is 1 with a standard deviation of 1.
E(X-Y) = E(X) - E(Y) = 30 - 29 = 1 TRUE
V(X-Y) = V(X) + V(Y) = 32 + 22 = 13
STD DEV (X-Y) = SQRT(V(X-Y)) = SQRT(13) = 3.61 FALSE
I-10TFFor the data in I-9, if X-Y is distributed normally, the probability a randomly selected male graduate has a higher starting salary than a random selected female graduate is .6103.
This is P(X-Y > 0) with = 1 and = 3.61