2022_PAPER_1_TEST_1

Extracted Content: 2022_PAPER_1_TEST_1

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General Certificate of Education Advanced Level

STATISTICS 6046/1
PAPER 1
REVISION TEST 1 2022 SESSION 3 hours
Additional materials:
Answer paper
Graph paper

List of formulae MF7
Electronic calculator (Non-programmable)

Time 3 hours

INSTRUCTIONS TO CANDIDATES

Write your name in the spaces provided on the answer sheet/answer booklet.

Answer all questions.

If anumerical answer cannot be given exactly, and the accuracy required is not specified in the
question, then in the case of an angle it should be given correct to the nearest degree, and in other
cases it should be given to 2 significant figures.

INFORMATION TO CANDIDATES

The number of marks is given in brackets [ | at the end of each question or part of question.
The total number of marks for this paper is 120.

The use of a scientific calculator is expected, where appropriate.

You are reminded of the need for clear presentation in your answers.

This question paper consists of 7 printed pages and 1 blank page.

Copyright: Sharewell B. C. (Share)—Share Online Revision Paper 1 2022

© Sharewell B. C. (Share)—Share Online Revision Paper 1 2022
Complied and typed by Share + 263784089807 [Turn Over

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1.

In a computer game played by a single player, the player has to find, within a fixed
time, the path through a maze shown on the computer screen. On the first occasion
that a particular player plays the game, the computer shows a simple maze, and the
probability that the player succeeds in finding the path in the time allowed is 0.75.
On subsequent occasions, the maze shown depends on the previous game. If the
player succeeded on the previous occasion, the next maze is harder, and the
probability that the player succeeds is one half of the probability of success on the
previous occasion. If the player failed on the previous occasion, a simple maze is

shown and the probability of the player succeeding is again 0.75.

The player plays three games.

a) Show that the probability that the player succeeds in all three games is =. [4]

b) Find the probability that the player succeeds in exactly one of the games. [3]
c) Find the probability that the player does not have two consecutive successes. [3]
d) Find the conditional probability that the player has two consecutive success

given that the player has exactly two successes. [3]

The amounts of money, x dollars, that 24 people had in their pockets are

summarized by (x — 36) = —60 and )\(x — 36)? = 227.76. Find }x and yx”. [5]

Acode consists of 10 digits, 4 of which are zeros and 6 of which are ones. Calculate
the number of such blocks in which the first and last digits are of the same as each

other. [4]

a) An unbiased tetrahedral die has faces marked 1, 2, 3, 4. If the die lands on the
face marked 1, the player has to play 10 USD.

If it lands on a face marked with a 2 or a 4, the player wins 5 USD and if it
lands on a 3, the player wins 3 USD. Find the expected gain in one throw. [5]

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b) A discrete random variable X can take values 10 and 20 only. If E(X)= 16,
write out the probability distribution of X. [7]

5. The continuous random variable H has continuous p.d.f. f(h) where

hi? 2sh<3
373 Shs
fWM= he 3<h<5
2-Bh 5<h<6
0 otherwise
Find
a) aandp [2]
b) F(h) and sketch y = F(h) [4]
c) P2<H <3.5) [2]

6. Arandom sample of St Dominic’s mathematics students marks for end of term test

are shown below.

67 76 85 42 93 48 93 46 52
72 77 53 41 48 86 78 56 80
70 70 66 62 54 85 60 58 43
58 74 44 52 74 52 82 78 47
66 50 67 87 78 86 94 63 72
63 44 47 57 68 81

a) Contract a stem a leaf diagram to represent these data. [6]
b) Find the median and the quartiles for this distribution. [6]
c) Draw a box plot to represent these data. [4]
d) Give one advantage of using

i) a stem and leaf diagram
ii) a box plot,

to illustrate data such as that given above. [2]

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7, Calculate the equation of the regression line x on y for the following distribution,

x 22 36 25 41 35 40
y 78 70 65 58 48 42

and the product-moment correlation coefficient, (7) and comment your value. [7]

a) Inacertain country, 68% of households have a printer. Find the probability

that, in a random sample of 8 households, 5, 6 or 7 households have a

printer.. [4]
b) Use an approximation to find the probability that, in a random sample of 500
households, more than 337 households have a printer. [4]
c) Justify your use of the approximation in part (b). [1]

9. Ina golf tournament, the number of times in a day that a ‘hole-in-one’ is scored is
denoted by the variable X, which has a Poisson distribution with mean 0.15. Mr
Kuna offers to pay $200 each time that a hole-in-one is scored during 5 days of play.

Find the expectation and variance of the amount that Mr Kuna pays. [4]

10. In the past, the flight time, in hours, for a particular flight has had mean 6.20 and
standard deviation 0.80. Some new regulations are introduced. In order to test
whether these new regulations have had any effect upon flight times, the mean flight

time for a random sample of 40 of these flights is found.

a) State what is meant by a Type! error in this context. [2]
b) The mean time for the sample of 40 flights is found to be 5.98 hours.
Assuming that the standard deviation of flight times is still 0.80 hours, test at

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the 5% significance level whether the population mean flight time has
changed. [4]
c) State, with a reason, which of the errors, Type I or Type II, might have been

made in your answer to part (b). [2]

11.
a) A petrol station finds that its daily sales, in litres, are normally distributed

with mean 4520 and standard deviation 560.

i) Find on how many days of the year (365 days) the daily sales can be
expected to exceed 3900 litres. [4]

The daily sales at another petrol station are X litres, where X is normally
distributed with mean m and standard deviation 560. It is given that

P(X > 8000) = 0.122.

ii) Find the value of m. [3]
iii) Find the probability that daily sales at this petrol station exceed 8000

litres on fewer than 2 of 6 randomly chosen days. [3]

b) The random variable Y is normally distributed with mean yp and standard
deviation o. Given that 0 = = u, find the probability that a random value of Y

is less than 2p. [3]

12. A firm of solicitors claims that, on average, interviews with clients last 50 minutes. A
random sample of 15 interviews is chosen, and the time taken for each interview, x
minutes, is noted. The results are summarized by }'.x = 746 and Y'x? = 37 180.
Assuming that the time for an interview has a normal distribution, determine at 5%

significance level, whether the firm is overstating the average interview. [6]

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13. The following data give the heights in centimeters of 100 male students.

Height (cm) | Frequency

155 — 160 5
161 — 166 17
167 — 172 38
173 — 178 25
179 — 184 9
185 — 190 6

Find the expected frequencies for a normal distribution having the same mean and
standard deviation as the data given, and test the goodness of fit, using a 5% level of

significance. [13]

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(— >)

FEEL FREE TO CONTACT ME FOR ANY ADJUSTMENTS, CLARIFICATIONS
AND ASSISTANCE!

schingwingwi7@gmail.com / +263784089807

Sharewell B. C

NN ,

“Concept before anything!”’, Author

Proverbs 11 vs. 2

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Complied and typed by Sharerwell B. Chingwingwi (Share)
+263784089807

schingwingwi7@qmail.com

[@2022]

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