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1. Find the probability of no accidents on this section of highway during a 1-week period.
2. Find the probability of at most three accidents on this section of highway during a 2-week period.
Q.No.5: A bag contains 14 identical balls, 4 of which are red, 5 black and 5 white. Six balls are drawn from the bag. Find the probability that:
(i) 3 are red, (ii) at least two are white
In a random selection of 64 of the 2400 intersections in a small city, the mean number of scooter accidents per year was 3.2 and the sample standard deviation was 0.8
a. Make an estimate of the standard deviation of the population from the sample standard deviation.
b. Work out the standard error of mean for this finite population.
c. If the desired confidence level is 0.90, what will be the upper and lower limit of the confidence interval for the mean number of accidents per intersection per year?
A fast-food restaurant has determined that the chance a customer will order a soft drink is 0.90. The probability that a customer will order a hamburger is 0.60. The probability that a customer will order French fries is 0.50.
(a) If a customer places an order, what is the probability that the order will include a soft drink and no French fries if these two events are independent?
(b) The restaurant has also determined that if a customer orders a hamburger, the probability the customer will also order fries is 0.80. Determine the probability that the order will include a hamburger and fries.
Three types of machine A, B and C, are used by a company to produce items which are very prone to a certain type of imperfection. A random sample of 100 items from each machine showed the number of perfect and imperfect items as follows:
Condition Machine
A B C
Perfect 33 39 48
Imperfect 67 61 52
Test whether there is evidence of significant association between machine type and proneness to imperfection. Use 5% level of significance.
(10 marks)
An automobile manufacturer collects mileage data for a sample of 10 cars in various weight categories by use of a standard grade of gasoline with and without a particular additive. The Engines were tuned to the same specifications before each run, and the same drivers were used for the two gasoline conditions (with the driver in fact being unaware of which gasoline was being used on a particular run). The mileage data is given in the table below:
Automobile 1 2 3 4 5 6 7 8 9 10
Mileage with Additive 36.5 36.1 32.0 29.3 28.4 25.7 24.2 22.6 21.0 20.3
Mileage without Additive 36.2 35.9 32.3 29.6 28.1 25.5 23.9 22.0 21.4 20.0
(a) test whether the additive is effective in increasing the mileage at 1% level of significance.
(12 marks)
(b) Do you think it is necessary to use the same drivers for two gasoline conditions? Explain your reasoning.
(3 marks)
Packets of instant coffee have a nominal weight of 32 grams. A random sample of 10 packets were selected and each of their weights, x grams, was recorded. It is found that:
∑▒x=305 , ∑▒x^2 =9505
(a) Find the unbiased estimate for the population mean and standard deviation.
(3 marks)
(b) A consumer association claimed that the mean weight of the instant coffee packet is less than 32 grams. Test at 5% significance level if this claim is true.
(8 marks)
Question 2
The efficiency of two training centres in a large organisation is to be evaluated. The examination results of a group of students from each centre on a common test are:
Centre X Y
Sample Size 50 40
Sample Mean 82.5 77
Sample Standard Deviation 7.2 9.1
Test at 1% level of significance, whether there is a significant difference in examination results between centres.
(8 marks)
1. What is the probability that the contestant wins?
2. Does the contestant’s probability of winning increases on the second round?
Create your own Games Fair game with 4 or more outcomes using a Hypergeometric situation and adjust the point values so that a cost of 10 points would make the game profitable.
#340153 on Dec 2023