Section AAnswer all questions in this section [45marks]

1. Each of the 25 students on a computer course recorded the number of minutes,x, spent on surfing the internet during a given day. The result summarized as below. , . a) Find for these data. [ 4 marks] b) Two other students surfed the internet on the same day for 35 and 51 minutes

respectively. Without further calculation, explain the effect on the mean of includingthese two student's time. [ 2 marks ]

2. a) Let X be the number of accidents in a factory per week such that

Show that P(X) is a probabilty distribution. [ 3 marks ] b) A coin is flipped 16 times. X is the number of times the head occur. Find the probability. (i) P ( X = 8 ) (ii) P ( X< 8 ) [ 4 marks ] 3. A teacher wishes to analyse the scores of students in a writen quiz. Ten randomly selected scores are 110,125,130,126,128,127,118,120,122,125. Assume the scores is normally distributed. a) Find the unbiased estimate for the mean and variance of the population. b) Calculate a 95% confidence interval for the mean of the population using a known

standard deviation of 5.5. c) The teacher wants the scores to be more than 130 marks. Comment whether the

teacher should be concerned about the scores of the students in the written quiz. [ 8 marks ]

4. A technician receives call to repair television sets at the mean of rate of 7 television sets per week.a) Give two reasons why the Poisson distribution is a suitable model to represent the number of calls to repair television sets in a randomly chosen week. [ 2 marks ]b) Find the probability that in any randomly chosen week, he reapairs exactly 5 television sets. [ 2 marks ]c) Using a suitable approximation, find the probabilty that during a 24 week period, the technician repairs more than 181 television sets. [ 4 marks ]

SMK Horley Methodist Teluk IntanTrial Examination Sem 3/ 2013

Mathematics T1 1/2 hours

5. In a study of the use of mobile phones among students, a random sample of 11 students was examined for a particular week. The total lenghth of calls made by 11 students were as follows. 17, 23, 35, 36, 51, 53, 54, 55, 60, 77, 110a) Find the median and quartiles for these data. [ 3 marks ]b) A value that is greater than Q3 +1.5(Q3 - Q1) or smaller than Q1 - 1.5 (Q3 - Q1) is defined as an outlier. Show that 110 is the only outlier. [ 2 marks ]c) Using a graph paper, draw a box - and - whisker plot showing all the information in parts (a) and (b). [ 3 marks ]

6. To serve a customer at a bank counter was estimated by the management as 12 minutes per customer. A random sample of 150 customers gave and where x is the time, in minutes, to serve a customer.a) Calculate the unbiased estimates of the population mean and variance.b) Stating the null dan alternative hypotheses, use 10% significance level to test whether the management's estimated time is consistent with the data. [ 8 marks ]

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Section BAnswer any one question in this section [ 15 marks ]

7. A continuous random variable X probability density function given by

a) Show that the value of k = 1/2b) Find the mean of Xc) Sketch the graph of f(x)d) Use the sketch to calculate median of Xe) State the mode of X [ 15 marks ]

8. The partially completed contigency table of observed values when doing a chi-squared test for indepence is as follows, where x is a positive integer:

Ability at playing badmintonGood Bad Totals

Ability at tennis Bad x 75Good 25Totals 60 40 100

a) Copy and complete the table by filling in the missing values in terms of x. [ 3 marks ]b) Complete a table for the expected values. [ 4 marks ]

c) Use the formula to calculate in terms of x, expressing

your answer in the form k(x - 45)2 where k is a fraction to be determined. [ 4 marks ]

d) Let the null hypothesis be the ability at playing badminton and tennis is independent. If the null hypothesis is accepted at 5% level of significance, find the possible values of x. [ 4 marks ]

Formulae

Binomial distribution

Poisson distribution

Chi- Squared test statistics

Good Luck !!!

Prepared by,

...........................Masytah bt Yazid

MAY/SEM3/2013/trial

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