Question

question 6: erin takes the bus to university 40 times during a term. the relative frequency of the bus being late is 0.3. how many times was the bus late? question 7: katie rolls a dice 100 times. the table shows the results. number: 1, 2, 3, 4, 5, 6; frequency: 22, 9, 14, 31, 19, 5. work out the relative frequency of throwing: (a) an even number (b) a square number (c) a prime number (d) a cube number (e) a multiple of 3 (f) a factor of 18. question 8: a spinner lands on white, black, red or orange. the relative frequencies after 300 spins are shown in the table below. colour: white, black, red, orange; relative frequency: 0.25, 0.4, 0.2, 0.15. (a) how many times did the spinner land on white? (b) how many times did the spinner land on red? (c) how many more times did the spinner land on black than orange? question 7: martin and laura want to estimate how many green jelly - beans are in a tub of 600 jelly beans. a trial consists of taking a jelly bean at random, noting the colour and replacing the jelly bean into the tub. number of trials: martin 30, laura 150; number of green jelly beans chosen: martin 4, laura 12. (a) write down the relative frequency of martin taking a green jelly bean. (b) write down the relative frequency of laura taking a green jelly bean. (c) whose experiment gives the more reliable estimate of the number of green jelly beans in the tub? give a reason for your answer. (d) how many green jelly beans do you expect to be in tub altogether?

Explanation:

Step1: Recall relative - frequency formula

Relative frequency = $\frac{\text{Frequency}}{\text{Total number of trials}}$

Step2: Solve for frequency

Frequency = Relative frequency $\times$ Total number of trials

Question 6

Total number of bus - trips $n = 40$, relative frequency of bus being late $rf=0.3$.
Frequency of bus being late $=0.3\times40 = 12$

Question 7

Total number of dice - rolls $n = 100$
(a) Even numbers are 2, 4, 6. Frequency of 2 is 9, of 4 is 31 and of 6 is 5. Total frequency of even numbers $f=9 + 31+5=45$. Relative frequency $=\frac{45}{100}=0.45$
(b) Square numbers are 1, 4. Frequency of 1 is 22 and of 4 is 31. Total frequency $f = 22+31 = 53$. Relative frequency $=\frac{53}{100}=0.53$
(c) Prime numbers are 2, 3, 5. Frequency of 2 is 9, of 3 is 14 and of 5 is 19. Total frequency $f=9 + 14+19 = 42$. Relative frequency $=\frac{42}{100}=0.42$
(d) Cube numbers are 1. Frequency is 22. Relative frequency $=\frac{22}{100}=0.22$
(e) Multiples of 3 are 3, 6. Frequency of 3 is 14 and of 6 is 5. Total frequency $f=14 + 5=19$. Relative frequency $=\frac{19}{100}=0.19$
(f) Factors of 18 are 1, 2, 3, 6. Frequency of 1 is 22, of 2 is 9, of 3 is 14 and of 6 is 5. Total frequency $f=22+9 + 14+5=50$. Relative frequency $=\frac{50}{100}=0.5$

Question 8

Total number of spins $n = 300$
(a) Relative frequency of red is 0.2. Number of times spinner landed on red $=0.2\times300 = 60$
(b) Relative frequency of black is 0.4 and of orange is 0.15. Number of times spinner landed on black $=0.4\times300 = 120$, on orange $=0.15\times300 = 45$. Difference $=120 - 45=75$

Question 7 (second set)

(a) Martin: Total number of trials $n = 30$, number of green jelly - beans $f = 4$. Relative frequency $=\frac{4}{30}=\frac{2}{15}\approx0.133$
(b) Laura: Total number of trials $n = 150$, number of green jelly - beans $f = 12$. Relative frequency $=\frac{12}{150}=0.08$
(c) Laura's experiment is more reliable as she has a larger number of trials. Larger sample size gives a more accurate estimate.
(d) Let the number of green jelly - beans in the tub be $x$. If we assume Laura's relative frequency is representative, and there are 600 jelly - beans in total. Then $0.08=\frac{x}{600}$, so $x=0.08\times600 = 48$

Answer:

Question 6: 12
Question 7 (a): 0.45
Question 7 (b): 0.53
Question 7 (c): 0.42
Question 7 (d): 0.22
Question 7 (e): 0.19
Question 7 (f): 0.5
Question 8 (a): 60
Question 8 (b): 75
Question 7 (second set a): $\frac{2}{15}\approx0.133$
Question 7 (second set b): 0.08
Question 7 (second set c): Laura, larger sample size
Question 7 (second set d): 48