This is for Quantative business analysis course. I need answers As soon as possi

Question

This is for Quantative business analysis course. I need answers As soon as possible thank you! Edit View ks W Help Me In Finally, place a header on the paper that includes your name, ID and section number (Section 5,6 or 7) and show your work for all questions to receive full credit. 8 points) In the United States, voters who are neither Democrat nor Republican are called Independents. It identify themselves as Democrat, Republican, or Independent a. What is the probability that none of the people are Independent? b. What is the probability that more than two people are Independent? 1. ( is believed that 15% of all voters are Independents. A survey asked 20 people to 2. (10 points) The final grades in a statistics course are normally distributed with a mean of 75 and a standard deviation of 10. The professor must convert all marks to letter grades. She decides that she wants 10% A's, 30% B's, 45% C's, 8% D's, and 7% F's. Determine the cutoffs for each letter grade. 3. (10 points) In older cities across North America, infrastructure is deteriorating, including water lines that supply homes and businesses. A report to a city council stated that there are on average 10 water line breaks per 100 kilometers per year in the city. Outside the city, the average number of breaks is 7 per 100 kilometers per year. a. Find the probability that in a stretch of 200 kilometers in a city there are 15 or more breaks next year b. Find the probability that there are 5 or fewer breaks in a stretch of 50 kilometers outside the city next year. 4. (12 points) The distributed between 8 and 15 minutes. One student is selected at random. Find the probability of amount of time it takes for a student to complete a statistics quiz is uniformly

Explanation / Answer

Question 1

Pr(Vote independent) = 0.15

Sample size n = 20

(i) If x is the number of people who voted to independent out of 20.

so,

Pr(x = 0) = BIN (x = 0 ; 20 ; 0.15) = 20C0 (0.15)0 (0.85)20 = 0.0388

(ii) Pr(x > 2 ; 20 ; 0.15) = 1 - BINCDF (x <= 2 ; 20 ; 0.15) = 1 - 0.4049 = 0.5951

Question 2

Here if x is the marks of any random student where

Mean of the marks = 75

Standard deviation of marks = 10

so Here as we know the percentage of students in each grade. Now we will associate each grade as its cumulative probability distribution. If x is the marks of any randomm student

so, for A's F(X) = 0.90

Z = 1.282

(X - 75)/10 = 1.282

X = 75 + 10 * 1.282 = 87.82

so for B's : F(X) = 1 - 0.10 - 0.30 = 0.60

so Z value = 0.2533

(X - 75)/10 = 0.2533

X = 75 + 10 * 0.2533 = 77.53

for C's : F(X) = 1 - 0.10 - 0.30 - 0.45 = 0.15

Z - value = -1.0364

(X - 75)/10 = -1.0364

X = 75 - 10 * 1.0364 = 64.64

for D's : F(X) = 1 - 0.10 - 0.30 - 0.45 - 0.08 = 0.07

Z- value = -1.4758

(X - 75)/10 = -1.4758

X = 75 - 10 * 1.4758 = 60.24

so now we ger cutoffs for each grade.

QUestion 3

(a) HEre expected number of line breaks in a stretch of 200 km in a city = 10 * 200/100 = 20

so if x is the total number of water line breaks in 200 km

so,

Pr(X >= 15) = 1- POISSON (x < 15 ; 20) = 1 - 0.1049 = 0.8951

(b) For outside the city, expected number of water line breaks in 50 km stretch = 50 * 7/100 = 3.5

so if x is the total number of water line breaks in 50 km outside the city

Pr(X <=5 ) = POISSON (X < = 5 ; 20) = 0.8576

Question 4

Here the time taken to complete the quiz is uniformly distributed in between 8 to 15 minutes.

so if x is the time taken to complete the quiz than

f(x) = 1/(15 - 8) = 1/7 ; 8 < x< 15

F(x) = (x - 8)/7 ; 8 < x < 15

= 1 ; x > 16

(i) so here

Pr(x > 13) =1 - Pr(x < 13) = 1 - (13 - 8)/7 = 2/7 = 0.286

(ii) Pr(10 < x < 16) = Pr(x < 16) - Pr(x < 10) = 1 - (10 - 8)/7 = 1 - 2/7 = 5/7 = 0.714

(iii) Pr(x = 9.1 minutes) = 1/7

(iv) For lowest quarter F(x) = 0.25

so F(x) = (x - 8)/7 = 0.25

x = 8 + 7 * 0.25 = 9.75 mins

Question 5

(i) P(Z < 0.6) = 0.7257

(ii) Pr(Z < = 1.23) = 0.8907

(iii) Pr(Z > 1.96) = 1- Pr(Z < 1.96) = 1 - 0.975 = 0.025

(iv) Pr(z < -2.0) = 0.02275

(v) Pr(Z > -1.645) = 1 - Pr(Z < -1.645)= 1 - 0.05 = 0.95

(vi) Pr( -1.96 < Z < 1.96) = Pr(Z < 1.96) - Pr(Z < -1.96) = 0.975 - 0.0225 = 0.95

(vii) Pr(Z > z) = 0.10

Pr(Z < z) = 1 - 0.10 = 0.90

z =1.645

(viii) Pr(-0.35 < z < 0.85) = Pr(Z < 0.85) - Pr(Z < -0.35) = 0.8023 - 0.3632 = 0.4391

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.