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ZIMSEC A Level · 6046/2 · N2018

Statistics Paper 2 November 2018

Questions
36
Total marks
152
Time allowed
180 min
Syllabus code
6046/2

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Questions
36
Pass mark
22
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Answer every question in the printed order, get marked at the end, then see the answers.

The questions

Question 101

[1 marks]data collection
Which of the following is an advantage of using telephone interviews as a way of collecting data?
  1. AThey remove the interviewer's influence on how respondents answer questions.
  2. BThey are quicker and cheaper to carry out than face-to-face interviews.
  3. CThey require the respondent to complete and post back a written form.
  4. DThey let the interviewer observe the respondent's body language directly.

Question 201

[1 marks]permutations and combinations
When selecting a number of objects from a set, which condition makes the selection a permutation rather than a combination?
  1. AWhen the order in which the objects are selected matters.
  2. BWhen the order in which the objects are selected does not matter.
  3. CWhen each object can be selected more than once in the same selection.
  4. DWhen the objects being selected are indistinguishable from one another.

Question 202

[1 marks]permutations and combinations
What is the formula, in terms of n and r, for the number of permutations of r objects chosen from n distinct objects?

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Question 301

[1 marks]probability
Whenever there is a power-cut, a school is equally likely (probability 1/3 each) to switch on one of its 3 generators A, B or C. The independent probabilities of a breakdown are 0.2 for A, 0.3 for B and 0.25 for C. For a randomly chosen day with a power-cut, what is the probability that there was a generator breakdown?
  1. A0.20
  2. B0.25
  3. C0.30
  4. D0.75

Question 302

[1 marks]probability
Using the same power-cut scenario (each generator equally likely to be switched on with probability 1/3; independent breakdown probabilities 0.2 for A, 0.3 for B, 0.25 for C), given that there was a generator breakdown, what is the probability that it was generator C?
  1. A0.250
  2. B0.300
  3. C0.333
  4. D0.375

Question 401

[1 marks]probability distributions
An unbiased die with faces marked 1, 2, 2, 3, 3, 3 is rolled twice. If X is the total score on the two rolls, what is P(X = 4), as a fraction out of 36?
  1. A9/36
  2. B12/36
  3. C6/36
  4. D10/36

Question 402

[1 marks]probability distributions
An unbiased die with faces marked 1, 2, 2, 3, 3, 3 is rolled twice. If X is the total score on the two rolls, what is the probability that X is a prime number, as a fraction out of 36?

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Question 403

[1 marks]probability distributions
For the same experiment (an unbiased die marked 1, 2, 2, 3, 3, 3 rolled twice, X = total score on the two rolls), what is E(X), to 3 decimal places?
  1. A4.000
  2. B4.333
  3. C4.667
  4. D5.000

Question 404

[1 marks]probability distributions
For the same experiment (an unbiased die marked 1, 2, 2, 3, 3, 3 rolled twice, X = total score on the two rolls), what is Var(X), to 3 decimal places?

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Question 501

[1 marks]continuous probability distributions
The mass X (in kg) of fish caught by a fisherman in a month has probability density function f(x)=ke−x/3f(x) = k e^{-x/3} for x≥0x \geq 0, and 0 otherwise. What is the value of k?
  1. A1/6
  2. B1/3
  3. C1/9
  4. D3

Question 502

[1 marks]continuous probability distributions
The mass X (in kg) of fish caught by a fisherman in a month has pdf f(x)=13e−x/3f(x) = \frac{1}{3} e^{-x/3} for x≥0x \geq 0. What is E(X)?

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Question 503

[1 marks]continuous probability distributions
For the same fish-mass distribution (f(x)=13e−x/3f(x) = \frac{1}{3} e^{-x/3} for x≥0x \geq 0), what is the probability that the fisherman catches at least 60 kg of fish, leaving the answer in exact form?

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Question 601

[1 marks]binomial and geometric distributions
In a certain school, 90% of learners are right handed. Using the Binomial distribution, what is the probability that in a random sample of 8 learners, exactly 6 are right handed, to 3 decimal places?
  1. A0.130
  2. B0.149
  3. C0.168
  4. D0.194

Question 602

[1 marks]binomial and geometric distributions
A discrete random variable X has a Geometric distribution with parameter P. Given that Var(X) = 12, what is the value of P, to 2 decimal places?

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Question 603

[1 marks]binomial and geometric distributions
A discrete random variable X follows a Geometric distribution with parameter P = 0.25 (found from Var(X) = 12). What is P(X > 3)?
  1. A0.250
  2. B0.422
  3. C0.563
  4. D0.750

Question 701

[1 marks]correlation and regression
For a data set with D: 0, 5, 10, 15, 20, 25, 30, 35 and corresponding M: 90, 82, 56, 68, 58, 46, 30, 20, what is the product moment correlation coefficient r, to 3 decimal places?

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Question 702

[1 marks]correlation and regression
For a data set with D: 0, 5, 10, 15, 20, 25, 30, 35 and corresponding M: 90, 82, 56, 68, 58, 46, 30, 20, the product moment correlation coefficient works out to r is approximately -0.957. Which statement best describes this correlation?
  1. ANo meaningful correlation between D and M.
  2. BStrong positive correlation between D and M.
  3. CStrong negative correlation between D and M.
  4. DWeak negative correlation between D and M.

Question 703

[1 marks]correlation and regression
Using the regression line of M on D fitted to the data D: 0, 5, 10, 15, 20, 25, 30, 35 and M: 90, 82, 56, 68, 58, 46, 30, 20, which works out to M = 89.17 - 1.881D, estimate M when D = 12, to 1 decimal place.

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Question 801

[1 marks]estimation and Poisson distribution
A random sample of 100 observations from a population gave ∑(x−50)=123.5\sum(x - 50) = 123.5. What is the unbiased estimate of the population mean μ\mu, to 3 decimal places?

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Question 802

[1 marks]estimation and Poisson distribution
A company receives on average 6 orders per day, following a Poisson distribution. What is the probability that no more than 2 orders will be received on a given day, to 3 decimal places?
  1. A0.045
  2. B0.062
  3. C0.089
  4. D0.120

Question 803

[1 marks]estimation and Poisson distribution
A company receives on average 6 orders per day, following a Poisson distribution. What is the probability that no orders are received during a given half day (mean 3 orders for the half day), to 3 decimal places?

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Question 901

[1 marks]normal distribution
The mass of a large loaf of bread is a Normal variable with mean 420 g and standard deviation 30 g. What is the probability that the total mass of 5 large loaves exceeds 2.1 kg?
  1. A0.159
  2. B0.250
  3. C0.500
  4. D0.750

Question 902

[1 marks]normal distribution
5 large loaves of bread (independent, Normal with mean 420 g and standard deviation 30 g each) and 10 small loaves (independent, Normal with mean 220 g and standard deviation 10 g each) are considered. What is the probability that the total mass of the 5 large loaves is less than the total mass of the 10 small loaves, to 3 decimal places?

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Question 903

[1 marks]normal distribution
A large loaf of bread has mass that is Normal with mean 420 g and standard deviation 30 g, and a small loaf has mass that is Normal with mean 220 g and standard deviation 10 g, independently of each other. What is the probability that a large loaf weighs more than twice the mass of a small loaf, to 3 decimal places?

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Question 1001

[1 marks]hypothesis testing
Which statement correctly distinguishes a statistic from a parameter?
  1. AA statistic is calculated from a sample, while a parameter describes the whole population.
  2. BA statistic describes the whole population, while a parameter is calculated from a sample.
  3. CA statistic and a parameter are both calculated only from sample data.
  4. DA parameter changes with every new sample taken, while a statistic stays fixed.

Question 1002

[1 marks]hypothesis testing
A sample of 10 toothpick lengths (cm): 4.99, 4.96, 5.00, 4.98, 5.01, 4.95, 4.96, 4.97, 4.99, 4.97 gives a sample mean of 4.978 cm and standard deviation of about 0.107 cm. Testing H0: mu = 5 against H1: mu is not equal to 5 at the 1% significance level gives a t-statistic of about -0.649, compared with a critical value of t(9) = 3.250. What is the conclusion?
  1. AReject H0 because the sample mean is exactly equal to 5 cm.
  2. BThe test is inconclusive and must be repeated with a larger sample.
  3. CReject H0; the machine is not producing toothpicks of the correct length.
  4. DDo not reject H0; there is insufficient evidence the machine is faulty.

Question 1003

[1 marks]hypothesis testing
A sample of 10 toothpick lengths (cm) is: 4.99, 4.96, 5.00, 4.98, 5.01, 4.95, 4.96, 4.97, 4.99, 4.97. What is the sample mean length, to 3 decimal places?

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Question 1101

[1 marks]time series
In time series analysis, which of the following best defines a 'trend'?
  1. AThe repeating pattern in the data that occurs at fixed points within each year.
  2. BThe general long-term movement in the data over time.
  3. CThe difference between the highest and lowest values recorded in the data.
  4. DThe random fluctuations in the data from one period to the next.

Question 1102

[1 marks]time series
Monthly sales ($) for a company were: January 700, February 200, March 300, April 800. What is the 3-month moving average of January, February and March sales?

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Question 1103

[1 marks]time series
Monthly sales ($) for a company were: July 1000, August 500, September 600. What is the 3-month moving average of July, August and September sales?

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Question 1201

[1 marks]chi-squared goodness of fit
A chi-squared goodness-of-fit test has 5 classes and is testing whether data follows a Normal distribution with a fully specified mean and standard deviation (neither estimated from the sample). How many degrees of freedom does the test statistic have?

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Question 1202

[1 marks]chi-squared goodness of fit
A chi-squared goodness-of-fit test (checking whether pupil heights follow a Normal distribution with mean 163 cm and standard deviation 4.4 cm) gives a test statistic of about 0.773 with 4 degrees of freedom, compared with a critical value of chi-squared(4) = 9.488 at the 5% level. What is the conclusion?
  1. ADo not reject H0; the data fits the stated distribution well.
  2. BReject H0; the pupils' heights do not follow the stated distribution.
  3. CReject H0 since the test statistic is larger than the critical value.
  4. DThe test cannot be used because expected frequencies are too small.

Question 1301

[1 marks]stem and leaf diagram
What is an advantage of using a stem-and-leaf diagram to present data, compared to a grouped frequency table?
  1. AIt needs far fewer original data points than a histogram would require.
  2. BIt automatically works out the mean and standard deviation of the data.
  3. CIt keeps the raw data visible while showing the distribution's shape too.
  4. DIt removes every extreme value (outlier) from the data set being presented.

Question 1302

[1 marks]stem and leaf diagram
30 learners reported their travel times to school (in minutes): 12, 10, 16, 8, 14, 18, 28, 33, 8, 40, 17, 27, 17, 22, 42, 7, 6, 43, 35, 20, 37, 19, 8, 47, 26, 16, 13, 11, 23, 46. How many of these learners took fewer than 10 minutes to travel to school?

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Question 1401

[1 marks]permutations and combinations
A packet contains 5 good fuses and 3 faulty fuses. In how many ways can 2 fuses be selected simultaneously from the packet?

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Question 1402

[1 marks]permutations and combinations
A packet contains 5 good fuses and 3 faulty fuses. Two fuses are selected simultaneously at random. What is the probability that exactly one of the two selected fuses is faulty?
  1. A0.357
  2. B0.375
  3. C0.500
  4. D0.536

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