Stpm Paper 3 2013t(u)
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STPM Mathematics T STPM 2013 ulangan P3 Section A [45 marks] Answer all questions in this section . 1. The stem-and- leaf diagram below shows the average int ake of fat weekly , in g rams, of 60 adult volunteers in a medical research. Stem Leaf 8 1 2 5 5 7 8 8 9 2 3 4 5 6 6 7 9 10 0 2 2 3 3 4 5 5 6 7 8 9 11 0 0 1 2 2 3 4 5 5 5 5 7 8 8 9 9 12 2 3 3 4 4 5 6 6 7 13 3 3 6 14 0 1 7 Key: 10 0 means 100 (a) Determine the median and the interquartile range of the distributio n. [4 marks] (b) Draw a box-and-whisk er plot to represent the data. [3 marks] (c) The above circled observation was recorded w rongly from its a ctual value o f 173. Show how this actual value affect your box-and-whisk er plot? [3 marks] 2. Two events A and B are such that P(A) = 1 7 , P(B) = 1 5 and PA U B) = 1 3 . Find P(B I A' ). [5 marks] 3. The discrete random variable X has the probability distribution as follows: X -60 20 24 60 P(X = x) p 0.10 q 0.25 It is given that P(X ≤ 20) = 0.25. (a) Determine the values of p and q. [2 marks] (b) Find E(X) and E {[X— E(X)] 2 }.[5 marks] 4. A random sample of 100 measurements taken f rom a population gives the fo llowing resu lts: 2 2980 ( ) 3168 x and x x . (a) Determine a 95% confidence interval for the population mean. [7 marks] (b) Suggest two ways to reduce the width of the confidence interval that you obtain. [2 marks] 5. Car panels are spray-painted by a machine. T he paint thickness on car panels is normally distributed w ith a mean of μ mm and a standard deviation of 0.035 mm. A random sample of 64 points paint thickness on car panels gives a mean of 0.195 mm. Test the null hypothesis H 0 : μ = 0.200 mm against the alternative hypothesis H 1 : μ ≠ 0.200 mm at the 5% significance level.[6 marks] 6. The power lines across a r ange of mountains ar e constant ly struc k by lightning. T he number of occurrence per week is recorded for the past 72 weeks. The results obtained are shown below. Number of lightning strikes per week 0 1 2 3 ≥ 4 Number of weeks 14 21 17 12 8 Perform a 2 goodness-of-fit test, at the 1% significance level, to determine whether the data fits a Poisson distribution with a mean of 2. [8 marks] You may use the probability distribution of a Poisson random variable with mean 2 given below. Number of occurrence 0 1 2 3 ≥ 4 7
Transcript of Stpm Paper 3 2013t(u)
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STPM Mathematics T STPM 2013 ulangan P3
Section A [45 marks]Answer all questions in this section
.1. The stem-and-leaf diagram below shows the average intake of fat weekly, in grams, of 60 adult volunteers in a
medical research.Stem Leaf
8 1 2 5 5 7 8 89 2 3 4 5 6 6 7 9
10 0 2 2 3 3 4 5 5 6 7 8 911 0 0 1 2 2 3 4 5 5 5 5 7 8 8 9 912 2 3 3 4 4 5 6 6 713 3 3 614 0 1 7
Key: 10 0 means 100
(a) Determine the median and the interquartile range of the distribution. [4 marks](b) Draw a box-and-whisker plot to represent the data. [3 marks]
(c) The above circled observation was recorded wrongly from its actual value of 173. Showhow this actual value affect your box-and-whisker plot? [3 marks]
2. Two events A and B are such that P(A) =1
7 , P(B) =
1
5 and PA U B) =
1
3. Find P(B I A' ). [5 marks]
3. The discrete random variable X has the probability distribution as follows:
X -60 20 24 60
P(X = x) p 0.10 q 0.25
It is given that P(X ≤ 20) = 0.25.(a) Determine the values of p and q. [2 marks]
(b) Find E(X) and E {[X— E(X)]2
}.[5 marks]
4. A random sample of 100 measurements taken from a population gives the following results:22980 ( ) 3168 x and x x .
(a) Determine a 95% confidence interval for the population mean. [7 marks](b) Suggest two ways to reduce the width of the confidence interval that you obtain. [2marks]
5. Car panels are spray-painted by a machine. The paint thickness on car panels is normally distributed with amean of μ mm and a standard deviation of 0.035 mm. A random sample of 64 points paint thickness on car
panels gives a mean of 0.195 mm. Test the null hypothesis H0 : μ = 0.200 mm against the alternative hypothesis
H1 : μ ≠ 0.200 mm at the 5% significance level.[6 marks]
6. The power lines across a range of mountains are constantly struck by lightning. The number of occurrence perweek is recorded for the past 72 weeks. The results obtained are shown below.
Number of lightning strikes per week 0 1 2 3 ≥ 4
Number of weeks 14 21 17 12 8
Perform a 2 goodness-of-fit test, at the 1% significance level, to determine whether the
data fits a Poisson distribution with a mean of 2. [8 marks]You may use the probability distribution of a Poisson random variable with mean 2 givenbelow.Number of occurrence 0 1 2 3 ≥ 4
7
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Probability 0.1353 0.2707 0.2707 0.1804 0.1429
Section B [15 marks] Answer only one question in this section.
7. (a) Describe briefly the standard normal random variable. [2 marks](b) The life span of a certain light bulb is a normal random variable with a mean of 950hours and a standard deviation of 50 hours.(i) Find the probability that a randomly chosen light bulb has a life span of more than 1000hours. [3 marks](ii) Determine the value of h such that 99% of the light bulbs have life span between (950 -h) hours and (950 + h) hours. [5 marks](iii) Find the probability that at most one out of eight independently selected light bulbs hasa life span of more than 1000 hours. [5 marks]
8. According to the National Health and Morbidity Survey study in 2006, the proportion of the population aged 30years and above suffering from diabetes is 0.15.
(a) A recent random sample of 20 persons aged 30 years and above shows that 4 of themare diabetic. Perform a hypothesis test, at the 10% significance level, to determine whetherthe current proportion of population aged 30 years and above who are suffering fromdiabetes is higher than that in 2006. [7 marks](b) In another random sample of 200 persons aged 30 years and above, 40 of them arefound to be diabetic. Perform a hypothesis test, at the 10% significance level, to determinewhether the current proportion of population aged 30 years and above who are sufferingfrom diabetes is higher than that in 2006. [8 marks]
