MATHEMATICAL METHODS UNIT 4
School Assessed Coursework 3 (SAC 3):
Problem-Solving Task 2 (Probability and Statistics)
Question 1 (47 marks)
Galaxian Highscore, the intrepid adventurer, buys all his strawberries in pa
...
MATHEMATICAL METHODS UNIT 4
School Assessed Coursework 3 (SAC 3):
Problem-Solving Task 2 (Probability and Statistics)
Question 1 (47 marks)
Galaxian Highscore, the intrepid adventurer, buys all his strawberries in packets from the Moles
supermarket. At Moles the number X of strawberries in a large packet is a discrete random variable
with probability distribution as shown in the following table:
x | 24 | 25 | 26 | 27
Pr( X=x) | 1
8 | 3 k2 | 3
8 | 14
+ka. Find all possible values of k. 3 marks
Question 1 - continued
PROBLEM SOLVING TASK Page 3
At the Moles supermarket the number Y of strawberries in a small packet is a discrete random variable
with probability distribution as shown in the following table:
y | 14 | 15 | 16 | 17
Pr(Y= y) | 0.21 | 0.38 | 0.23 | 0.18b. Galaxian buys two small packets of strawberries.
Find the probability, correct to four decimal places, that
i. each packet has 14 strawberries. 1 mark
ii. the total number of strawberries in both packets is equal to 32. 2 marks
iii. if the total number of strawberries in both packets is equal to 32 then one of the packets has
15 strawberries 3 marks
Question 1 - continued
TURN OVER
PROBLEM SOLVING TASK Page 4
c. On another occasion Galaxian buys seven small packets of strawberries.
Find the probability, correct to four decimal places, that
i. at least three of the packets have 16 strawberries. 2 marks
ii. if at least two of the packets have 16 strawberries then exactly four of the packets have 16
strawberries. 3 marks
Question 1 - continued
PROBLEM SOLVING TASK Page 5
Max Hardcase, the steadfast partner-in-adventure of Galaxian Highscore, also buys all his
strawberries from the Moles supermarket. He buys a number of small packets of strawberries in
readiness for a new adventure.
d. i. Find the smallest number of packets that Max could have bought if the probability that at
least 10 of his packets have less than 16 strawberries is greater than 0.9 3 marks
A regular strawberry has a width of at least 2 cm. One of the small packets that Max buys has 15
strawberries in it and 12 of those strawberries are regular.
ii. Max selects a random sample of 11 strawberries from this packet. Find the probability that
more than 8 of the strawberries in the sample are regular. 3 marks
Question 1 - continued
TURN OVER
PROBLEM SOLVING TASK Page 6
Moles supermarket claims that 90% of all the strawberries it sells are regular.
Galaxian Highscore collects a random sample of 51 strawberries after buying two large packets.
e. i. Find, correct to four decimal places, the probability that at least 44 of the strawberries
in his sample are regular.
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