Danho
ZIMSEC A Level · 6046/2 · N2022

Statistics Paper 2 November 2022

Questions
30
Total marks
152
Time allowed
180 min
Syllabus code
6046/2

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Questions
30
Pass mark
18
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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]normal distribution
The volume of dish washing liquid in satchets is normally distributed with mean 400 ml and standard deviation 45 ml, independent of the volume of fabric softener in bottles, which is normally distributed with mean 650 ml and standard deviation 50 ml. Let W be the total volume of 2 randomly chosen bottles of fabric softener minus the total volume of 4 randomly chosen satchets of dish washing liquid. What is the standard deviation of W, in ml (to 1 decimal place)?
  1. A67.3 ml
  2. B114.5 ml
  3. C118.5 ml
  4. D280.0 ml

Question 102

[1 marks]normal distribution
A new detergent is made by mixing the contents of 1 satchet of dish washing liquid, mean volume 400 ml, with 2 bottles of fabric softener, mean volume 650 ml per bottle. What is the expected total volume of the new detergent, in ml?
  1. A1700 ml
  2. B2100 ml
  3. C1050 ml
  4. D1300 ml

Question 201

[1 marks]normal distribution
A machine packs washing powder into packets with mean weight 2 kg. The weights are normally distributed, and 10% of packets weigh less than 1,95 kg. What is the standard deviation of the packet weights, in kg (to 3 decimal places)?
  1. A0.025 kg
  2. B0.030 kg
  3. C0.039 kg
  4. D0.064 kg

Question 202

[1 marks]normal distribution
Packets of washing powder have weights normally distributed with mean 2 kg and standard deviation 0,039 kg. What proportion of packets weigh more than 2,10 kg? Give your answer to 3 decimal places or as a percentage.

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Question 301

[1 marks]continuous random variables
A continuous random variable X has probability density function f(x) = (3/8)x^2 for 0 <= x <= 2. What is the cumulative distribution function F(x) for 0 <= x <= 2?
  1. AF(x) = x^2/8
  2. BF(x) = 3x^2/8
  3. CF(x) = x^3/6
  4. DF(x) = x^3/8

Question 302

[1 marks]continuous random variables
A continuous random variable X has cumulative distribution function F(x) = x^3/8 for 0 <= x <= 2. What is the median m of X? Give your answer to 3 decimal places.

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Question 401

[1 marks]normal distribution
A normal random variable Y has mean mu and standard deviation sigma. Given that P(Y > 34) = 0,0228, so (34 - mu)/sigma = 2,00, and P(Y < 25) = 0,0062, so (25 - mu)/sigma = -2,50, find sigma.

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Question 402

[1 marks]normal distribution
A normal random variable Y has mean mu and standard deviation sigma = 2. Given that P(Y > 34) = 0,0228, so (34 - mu)/sigma = 2,00, find mu.

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Question 501

[1 marks]confidence intervals
Ten measurements of x, the burning time in hours of a particular make of candle, gave the sum of (x - 5) equal to 12,5. What is the sample mean x-bar?

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Question 502

[1 marks]confidence intervals
A 95% confidence interval for a population mean is constructed from a sample of 10 measurements using the t-distribution, because the population standard deviation is unknown and the sample is small. How many degrees of freedom does the t-distribution have?
  1. A8
  2. B9
  3. C10
  4. D11

Question 503

[1 marks]confidence intervals
Ten measurements of x, the burning time in hours of a particular make of candle, gave the sum of (x - 5) equal to 12,5 and the sum of (x - 5)^2 equal to 23,8. What is the sample variance s^2? Give your answer to 3 decimal places.

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Question 601

[1 marks]normal distribution
Mrs Moyo's time in the clinic is normally distributed with mean 25 minutes and standard deviation 4 minutes. What is the probability that she is in the clinic for more than 28 minutes on a particular day? Give your answer to 4 decimal places.
  1. A0.1056
  2. B0.2266
  3. C0.4013
  4. D0.7734

Question 602

[1 marks]normal distribution
Mrs Moyo's travel time to the clinic is normally distributed with mean 15 minutes and standard deviation 2 minutes, independent of her time in the clinic, which is normally distributed with mean 25 minutes and standard deviation 4 minutes. What is the probability that on a particular day she spends more time travelling than she spends in the clinic? Give your answer to 4 decimal places.
  1. A0.0127
  2. B0.2266
  3. C0.5000
  4. D0.9873

Question 701

[1 marks]probability and Poisson distribution
Alan and Alex play a game firing at a target alternately, with Alan firing first. Each has a probability of 0,6 of hitting the target on any given shot. What is the probability that Alan hits the target on his 2nd shot, meaning Alan misses his 1st shot, Alex misses his 1st shot, then Alan hits his 2nd shot?
  1. A0.096
  2. B0.160
  3. C0.240
  4. D0.360

Question 702

[1 marks]probability and Poisson distribution
Alan and Alex play a game firing at a target alternately, with Alan firing first. The first one to hit the target wins the game, and each has a probability of 0,6 of hitting the target on any given shot. What is the probability that Alan wins the game? Give your answer as a fraction or to 3 decimal places.

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Question 703

[1 marks]probability and Poisson distribution
The number of spelling errors per page in the first draft of a long assignment follows a Poisson distribution with mean 0,3. What is the probability that a randomly chosen page contains no spelling error? Give your answer to 4 decimal places.
  1. A0.2592
  2. B0.3000
  3. C0.7408
  4. D0.9048

Question 801

[1 marks]cumulative frequency
Steel rod lengths were measured to the nearest mm and grouped into classes, the shortest being 92-93 mm. What is the least possible actual length, in mm, of a rod recorded in this class?
  1. A91.0 mm
  2. B91.5 mm
  3. C92.0 mm
  4. D92.5 mm

Question 802

[1 marks]cumulative frequency
Steel rod lengths were measured to the nearest mm and grouped into classes, the longest being 102-103 mm. What is the greatest possible actual length, in mm, of a rod recorded in this class?

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Question 803

[1 marks]cumulative frequency
A sample of 80 steel rods had lengths measured to the nearest mm: 2 rods in the 92-93 mm class and 7 rods in the 94-95 mm class, so the cumulative frequency is 2 rods up to 93,5 mm and 9 rods up to 95,5 mm. A rod is rejected if its actual length is less than 94,5 mm. Using linear interpolation between these two cumulative frequencies, estimate the percentage of rods that have to be rejected.

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Question 901

[1 marks]Poisson distribution / chi-squared goodness of fit
The number of telephone calls received at a switchboard per 10-minute period was recorded as follows: 8 periods with 0 calls, 19 with 1 call, 26 with 2 calls, 13 with 3 calls, 7 with 4 calls, 5 with 5 calls, 1 with 6 calls, 1 with 7 calls, and 0 with 8 calls. What is the mean number of calls per 10-minute period?

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Question 902

[1 marks]Poisson distribution / chi-squared goodness of fit
When testing whether a Poisson distribution is a good fit to observed data using a chi-squared goodness-of-fit test, a class with an expected frequency below 5 is usually...
  1. Aremoved from the data set entirely before the test statistic is calculated
  2. Breplaced by the value of the overall sample mean before comparing the frequencies
  3. Ccombined with a neighbouring class so the expected frequency reaches at least 5
  4. Dleft unchanged, since small expected frequencies do not affect the test statistic

Question 1001

[1 marks]time series
Daily egg sales, in crates, at a supermarket were Monday 2, Tuesday 5, Wednesday 4, Thursday 4, Friday 9, Saturday 7, Sunday 6, Monday 8. What is the 3-point moving average centred on Tuesday, calculated from Monday, Tuesday and Wednesday?

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Question 1002

[1 marks]time series
Daily egg sales, in crates, at a supermarket were Monday 2, Tuesday 5, Wednesday 4, Thursday 4, Friday 9, Saturday 7, Sunday 6, Monday 8. What is the 3-point moving average centred on Saturday, calculated from Friday, Saturday and Sunday?

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Question 1003

[1 marks]time series
A time series is best defined as...
  1. Aa sequence of data values recorded at successive, equally spaced points in time
  2. Ba set of data values recorded from different individuals at a single point in time
  3. Cthe correlation between two variables that are both measured over the same time period
  4. Dthe arithmetic mean of a data set that has been collected repeatedly over several periods

Question 1101

[1 marks]probability
In a group of A-level students, 63% are boys and the probability of a boy studying Mathematics is 1/9. What is the probability that a student selected at random from this group is a boy studying Mathematics?

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Question 1102

[1 marks]probability
In a group of A-level students, 63% are boys with probability 1/9 of studying Mathematics, and 37% are girls with probability 2/7 of studying Mathematics. What is the probability that a student selected at random from this group is not studying Mathematics? Give your answer to 3 decimal places.
  1. A0.176
  2. B0.700
  3. C0.824
  4. D0.930

Question 1103

[1 marks]probability
In a group of A-level students, 63% are boys with probability 1/9 of studying Mathematics, and 37% are girls with probability 2/7 of studying Mathematics, so P(girl and Mathematics) is approximately 0,1057 and P(Mathematics) is approximately 0,1757. What is the probability that a Mathematics student selected at random from this group is female? Give your answer to 3 decimal places.

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Question 1201

[1 marks]regression and correlation
For a bivariate data set, Sxy = 3462,3 and Sxx = 3352,1. What is the gradient of the regression line of y on x? Give your answer to 3 decimal places.

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Question 1202

[1 marks]regression and correlation
For a bivariate data set, the mean of x is 55,7, the mean of y is 66,1, and the gradient of the regression line of y on x is 1,033. What is the y-intercept of this regression line? Give your answer to 2 decimal places.

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Question 1203

[1 marks]regression and correlation
The product moment correlation coefficient between two students' Sociology and Economics exam marks was calculated as approximately 0,99. This value indicates...
  1. Aa weak positive linear relationship between the two sets of marks
  2. Bno meaningful linear relationship between the two sets of marks
  3. Ca very strong negative linear relationship between the two sets of marks
  4. Da very strong positive linear relationship between the two sets of marks

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