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WorksheetsTest 2 semester 3
Total questions: 19
Worksheet time: 56mins
5.18
5.12
5.04
5.45
According to a firm’s internal survey, of those employees living more than 5 km from work, 90% travel to work by car. Of the remaining employees, only 50% travel to work by car. It is known that 75% of employees live more than 5 km from work. Determine
The overall proportion of the employees who travel to work by car
0.3
0.8
0.5
0.9
According to a firm’s internal survey, of those employees living more than 5 km from work, 90% travel to work by car. Of the remaining employees, only 50% travel to work by car. It is known that 75% of employees live more than 5 km from work. Meanwhile, the overall proportion of the employees who travel to work by car is 0.8. Find the probability that an employee who travels to work by car lives more than 5 km from work.
0.6392
0.7365
0.8438
0.9725
State the mode of X
1.5
0
2
1
Give a reason why a ≥ b
f(x) ≥ 0 for all x
f(0) = a - b ≥ 0 , a ≥ b
f(x) ≥ 1 for all x
f(1) = a - b ≥ 0 , a ≥ b
Find 3a-b
2
3/2
3
1/2
Given that b=3/8, the upper quartile of X is....
square root 6
square root 3
square root 5
square root 2
150 bags of flour of a particular brand are weighed and the mean mass is found to be 748 g with standard deviation 3.6 g. Do you need to do unbiased estimates for standard deviation in order to find 95% confidence intervals for the mean mass of bags of flour of this brand?
yes
no
Test, at the 5% significance level whether the mean mass of the contents of a bag is less than 10 kg
-1.495 > -1.645. Fail To Reject Ho
1.795 > 1.645. Reject Ho
-1.795 < -1.645. Reject Ho
1.495 < 1.645. Fail To Reject Ho
Explain the meaning of ‘at the 5% significance level’
the probability of the context that rejects the hypothesis that the mean mass of the contents of a bag with 10 kg, when it is in fact actually true Is 5%.
the probability of the context that fail to reject the hypothesis that the mean mass of the contents of a bag with 10 kg, when it is in fact actually false Is 5%.
at the 1% significance level, is the quality of work depends on condition?
14.79>13.28. At 1% significance level, the data provides sufficient evidence that the quality of work is not independent on condition.
12.79<13.28.At 1% significance level, the data provides insufficient evidence that the quality of work is not independent on condition.
15.67>13.28. At 1% significance level, the data provides sufficient evidence that the quality of work is not independent on condition.
11.67<13.28. At 1% significance level, the data provides insufficient evidence that the quality of work is not independent on condition.
A test is carried out to show that the data provide evidence, at the 1% significance level, that quality of work depends on condition. Can you concluded that better work is produced under good conditions than under poor conditions?
Yes. The above test reflect the actual relationship between the two factors because they are not independent of each other.
No. The above test does not reflect the actual relationship between the two factors but merely conclude that they are not independent of each other.
4. The random variable X has a Poisson distribution with mean 𝝺. Given that
P(X = 1) = 3P(X = 0),
Find the value of 𝝺
2
3
1
4
4. The random variable X has a Poisson distribution with mean 3. Given that
P(X = 1) = 3P(X = 0),
calculate P(X > 2),
0.629
0.482
0.577
0.228
When a machine is used to dig up potatoes there is a probability 0.1 for each individual potato it will be damaged in the process.
Find, correct to 3 decimal places, the probability that a random selection of 12 potatoes dug up by machine will include at least 3 damaged ones.
0.333
0.222
0.111
0.444
When a machine is used to dig up potatoes there is a probability 0.1 for each individual potato it will be damaged in the process. A random sample of n potatoes is selected, and the number of damaged potatoes in the sample is denoted by the random variable X. Write down expressions, in terms of n, for the mean and standard deviation of X.
Mean = E(X) = 0.1n, S.D = 0.2√n
Mean = E(X) = 0.1n, S.D = 0.3√n
Mean = E(X) = 0.1/n, S.D = 0.3√n
Mean = E(X) = 0.1/n, S.D = 0.3/√n
A telephone enquiry service is so busy that only 80% of incoming calls are successfully connected. It may be assumed that all calls are independent. Twelve calls are made at random to the service. Find the probability that at least 9 are successfully connected.
0.529
0.861
0.629
0.795
4. A telephone enquiry service is so busy that only 80% of incoming calls are successfully connected. It may be assumed that all calls are independent.
After improving the facilities, the management arranges for a random sample of 120 calls to be made to the service and it is found that 105 of these calls are successfully connected. Test, at the 4% significance level, whether the successful connection rate has improved.
1.054 <1.751 Fail to reject H0
At 4% significance level, there is insufficient evidence to conclude that the successful connection rate has improved.
2.864 >1.645 Reject H0
At 4% significance level, there is sufficient evidence to conclude that the successful connection rate has improved.
2.054 >1.751 Reject H0
At 4% significance level, there is sufficient evidence to conclude that the successful connection rate has improved.
1.054 <1.645 Fail to reject H0
At 4% significance level, there is insufficient evidence to conclude that the successful connection rate has improved.
A consumer association carries out its own test using a random sample of 150 calls and finds that the number of unsuccessful calls is 25. Using this sample, find an approximate 92% confidence interval for the proportion of calls that are unsuccessful.
(0.113, 0.220)
(0.123, 0.320)
(0.114, 0.225)
(0.163, 0.370)
