Question
The number of hours spent exercising each week by a group of students is shown in the following table.
The median is 4.5 hours.
(a) Find the value of x .
(b) Find the standard deviation.
Answer/Explanation
Ans:
(a) EITHER
recognising that half the total frequency is 10 (may be seen in an ordered list or indicated on the frequency table)
OR
5 + 1 + 4 = 3 + x
OR
\(\sum f = 20\)
THEN
x = 7
(b) METHOD 1
1.58429…
1.58
METHOD 2
EITHER
Question
A discrete random variable, X, has the following probability distribution:
(a) Show that 2k2 – k + 0.12 = 0.
(b) Find the value of k , giving a reason for your answer.
(c) Hence, find E(X).
Answer/Explanation
Ans:
(a) 0.41 + k – 0.28 + 0.46 + 0.29 – 2k2 = 1 OR k – 2k2 + 0.01 = 0.13 (or equivalent)
2k2 – k + 0.12 = 0
(b) one of 0.2 OR 0.3
k = 0.3
reasoning to reject k = 0.2 eg P(1) = k – 0.28 0 ≥ 0 therefore k ≠ 0.2
(c) attempting to use the expected value formula
E(X) = 0 × 0.41 + 1 × (0.3 – 0.28) + 2 × 0.46 + 3 ×(0.29 – 2 × 0.32)
= 1.27
Note: Award M1A0 if additional values are given.