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iii) In a small town, two lawn companies fertilize lawns during the summer. Tri-State Lawn Service has 72% of the market. Thirty percent of the lawns fertilized by Tri-State could be rated as very healthy one month after service. Greenchem has the other 28% of the market. Twenty percent of the lawns fertilized by Greenchem could be rated as very healthy one month after service. A lawn that has been treated with fertilizer by one of these companies within the last month is selected randomly. If the lawn is rated as very healthy, what are the revised probabilities that Tri-State or Greenchem treated the lawn?
b. What is the probability that the senior executive does not agree or strongly agree that gender-based stereotypes were barriers to her career development given that she does agree or strongly agree that the lack of role models was a barrier to her career development?
c. If it is known that the senior executive does not agree or strongly agree that gender-based stereotypes were barriers to her career development, what is the probability that she does not agree or strongly agree that the lack of role models was a barrier to her career development?
iii) The U.S. Energy Department states that 60% of all U.S. households have ceiling fans. In addition, 29% of all U.S. households have an outdoor grill. Suppose 13% of all U.S. households have both a ceiling fan and an outdoor grill. A U.S. household is randomly selected.
a. What is the probability that the household has a ceiling fan or an outdoor grill?
b. What is the probability that the household has neither a ceiling fan nor an outdoor grill?
c. What is the probability that the household does not have a ceiling fan and does have an outdoor grill?
d. What is the probability that the household does have a ceiling fan and does not have an outdoor grill?
A researcher wants to understand how an annual mortgage payment (in Ringgit) depends on income level and zonal location allowing for interaction. The data are shown as below.
LOW
MEDIUM
HIGH
KOTA KINABALU
130
186
231
128
201
216
201
195
171
190
186
216
150
191
186
SANDAKAN
126
218
306
220
263
351
260
230
330
311
308
486
280
314
498
TAWAU
233
171
231
173
186
186
131
21
243
128
306
201
77
231
207
LAHAD DATU
120
183
231
180
96
156
160
141
168
130
126
141
80
105
110
KENINGAU
13
46
65
18
31
36
18
46
51
23
41
46
26
41
39
a) Determine the total sum of square income (factor A), sum of square for zonal location (factor B), sum of square for the interaction between income and zonal location, and error sum of square. 10 marks
b) Determine the F-Statistics and P-Value for income, zonal location and interaction between income and zonal location. 6 marks
Q.No.2 i. According to Nielsen Media Research, approximately 67% of all U.S. households with television have cable TV. Seventy-four percent of all U.S. households with television have two or more TV sets. Suppose 55% of all U.S. households with television have cable TV and two or more TV sets. A U.S. household with television is randomly selected.
a. What is the probability that the household has cable TV or two or more TV sets?
b. What is the probability that the household has cable TV or two or more TV sets but not both?
c. What is the probability that the household has neither cable TV nor two or more TV sets?
d. Why does the special law of addition not apply to this problem?
ii) a. A batch of50 parts contains six defects. If two parts are drawn randomly one at a time without replacement, what is the probability that both parts are defective?
b. If this experiment is repeated, with replacement, what is the probability that both parts are defective?
Q.No.1 i. A supplier shipped a lot of six parts to a company. The lot contained three defective parts. Suppose the customer decided to randomly select two parts and test them for defects. How large a sample space is the customer potentially working with? List the sample space. Using the sample space list, determine the probability that the customer will select a sample with exactly one defect.
ii. A bin contains six parts. Two of the parts are defective and four are acceptable. If three of the six parts are selected from the bin, how large is the sample space? Which counting rule did you use, and why? For this sample space, what is the probability that exactly one of the three sampled parts is defective?
iii. A company places a seven-digit serial number on each part that is made. Each digit of the serial number can be any number from 0 through 9.Digits can be repeated in the serial number. How many different serial numbers are possible?
An integer between 5 and 40 (both exclu Suppose sive) is chosen at random. What is the probability that
i. It is an odd number?
ii. It is an even number and divisible by 4.
A researcher reports that the average salary of College Deans is more than P63,000. A sample of 35 College Deans has a mean salary of P65, 700. At , test the claim that the College Deans earn more than P63,000 a month. The standard deviation of the population is P5,250.
The theory predicts that the population of beans in the four groups A,B, C and D
should be 9:3:3:1. In an experiment among 1600 beans,the number in the four
groups was 882,313,287 and 118. Do theexperimental results support the survey
Samples of 4 cards are drawn from a population of 6 cards numbered 1-6. Construct a sampling distribution of the sample means and answer the following questions:
1. How many samples of size 4 can be drawn from the population?
2. What are the possible means?
3. What is the probability of getting 4 as a mean?
4. What is the probability of getting 3.5 as a mean?
