STAT 3360 | HOMEWORK 5 | Complete Solution

HOMEWORK 5 – STAT 3360

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READ SECTIONS 7.4 – 7.5
BEFORE YOU START SOLVING THESE PROBLEMS. TABLE 2 IS REQUIRED.
SECTION [CIRCLE ONE! =>] 002 003 001
FIRST NAME LAST NAME
PROBLEM 1 [30 POINTS = 5+5+5+5+5+5]

TOM AND JERRY DECIDED TO PLAY A MATCH OF 6 TENNIS GAMES. HISTORICALLY THEY HAVE ASSESSED JERRY’S WINNING CHANCES AS 40%, WHILE TOM WINS 60% OF THEIR GAMES. CONSIDER A RANDOM VARIABLE (W) THAT SHOWS THE NUMBER OF GAMES WON BY TOM. THEREFORE (6 – W) IS THE NUMBER OF GAMES LOST BY TOM. SEPARATE GAMES ARE VIEWED AS INDEPENDENT TRIALS. SHOW THE FORMULA THAT YOU USE IN EACH CASE

.
1. WHAT IS THE CHANCE THAT TOM WINS AT MOST 5 OUR OF 6 GAMES?
P [W ≤ 5] =
2. WHAT IS THE CHANCE THAT TOM WINS AT LEAST 1 OUT OF 6 GAMES?
P [W ≥ 1] =
3. HOW MANY GAMES DOES TOM EXPECT TO WIN?
E [W] =
4. WHAT IS THE VARIANCE OF THE RANDOM VARIABLE W?
VAR [W] =
5. IF TOM IS GAINING $3 FOR EACH VICTORY AND LOSING $4 FOR EACH
GAME HE HAS LOST, HOW MUCH MONEY DOES HE EXPECT TO WIN? FIND
THE EXPECTATION OF Z = [3 W – 4 (6 – W)] = 7W – 24.
E [Z] =
ALSO DETERMINE THE VARIANCE AND STANDARD DEVIATION OF Z.
VAR [Z] =
SD [Z] =
6. WHAT IS THE STANDARD DEVIATION OF (6 – W), THE NUMBER OF
GAMES LOST BY TOM?
SD [6 – W] =
HOMEWORK 5 – STAT 3360 – SPRING 2015
DUE BY FEBRUARY 26 [SECTIONS 002, 003] AND BY MARCH 2 [SECTION 001]
PLEASE, SUBMIT THIS DOCUMENT AND SHOW YOUR FIRST AND LAST NAME BELOW!
STAPLE OR PAPERCLIP YOUR WORK, PLEASE!

PROBLEM 2 [30 POINTS = 10+10+10]
A CAR DEALERSHIP HIRED JOHN AS SALES ANALYST TO ASSESS RISKS. JOHN ASSUMES THAT A NUMBER OF CARS SOLD BY ONE SALESPERSON DURING A CERTAIN PERIOD OF TIME FOLLOWS THE POISSON DISTRIBUTION WITH THE INTENSITY = 0.22 CAR/DAY. A RANDOM VARIABLE (X) MEASURES THE NUMBER OF CARS SOLD BY ONE PERSON AFTER 25 DAYS.
1. WHAT IS THE CHANCE TO SELL MORE THAN 6 CARS DURING THE 25-DAY PERIOD, I.E. HOW LIKELY WILL X BE HIGHER THAN 6? P [X > 6] =
2. WHAT PROPORTION OF SALES PERSONNEL IS EXPECTED TO SELL AT LEAST 4 AND AT MOST 10 CARS DURING THE 25-DAY PERIOD? P [4 ≤ X ≤ 10] =
3. WHAT IS THE CHANCE TO SELL FEWER THAN 12 CARS DURING THE 25-DAY PERIOD? P [X < 12] =
HOMEWORK 5 – STAT 3360 – SPRING 2015
DUE BY FEBRUARY 26 [SECTIONS 002, 003] AND BY MARCH 2 [SECTION 001]
PLEASE, SUBMIT THIS DOCUMENT AND SHOW YOUR FIRST AND LAST NAME BELOW!
STAPLE OR PAPERCLIP YOUR WORK, PLEASE!

PROBLEM 3 [40 POINTS = 10 + 10 + 10 + 10]
DEPARTMENT OF PUBLIC SAFETY ANALYSTS ARE ASSESSING RISKS ON HIGHWAYS. THEY ASSUME THAT THE EXPECTED NUMBER (INTENSITY) OF CAR COLLISIONS DURING RUSH HOURS IS MEASURED AS 0.2 PER DAY. DURING A 30-DAY PERIOD, THE VARIABLE (Y) IS GOING TO BE OBTAINED AS A TOTAL NUMBER OF CAR COLLISIONS.
1. DESCRIBE THE DISTRIBUTION OF Y.WHAT PARAMETER YOU ARE GOING TO USE EVALUATING PROBABILITIES OF Y VALUES? PARAMETER =
2. WHAT IS THE CHANCE TO HAVE MORE THAN 8 CAR COLLISIONS DURING THE 30-DAY PERIOD, I.E. HOW LIKELY WILL Y BE HIGHER THAN 8? P [Y > 8] =
3. WHAT IS THE CHANCE OF FINDING AT LEAST 5 AND AT MOST 11 CAR COLLISIONS DURING THE 30-DAY PERIOD? P [5 ≤ Y ≤ 11] =
4. WHAT IS THE CHANCE OF FINDING FEWER THAN 11 AND MORE THAN 5 CAR COLLISIONS DURING THE 30-DAY PERIOD? P [5 < Y < 11] =
PROBLEM
1
2
3
TOTAL
POINTS
MAXIMUM
30
30
40
100