Search & Filtering
A researcher would like to test whether there is any significant difference between the proportion of
safety consciousness of men and women while driving a car. In a sample of 300 men, 130 said that
they used seat belts. In a sample of 300 women, 90 said that they used seat belts. Test the claim that
there is no significant difference between the proportion of safety consciousness of men and women
while driving a car at 5% level of significance. (Given that Z0.025 = 1.96)
- QUESTION FOUR [20] 4.1 A box contains balls, drawn at random. (The first ball is not replaced). Find the probability that both balls are of the same colour. (4) 5 red 6 white balls and 9 black balls. Two balls are 4.2 At the Durban beachfront of days. If rain it rains on 20% of days and it is windy on 30% and wind are independent, any particular day find the probability that: 4.2.1 it rains and is windy. (3) 4.2.2 it does not rain and is not windy. (3) 4.2.3 it rains or is windy. (3) 4.2.4 it does not rain or is not windy. (3) 4.3 Draw a Venn diagram to illustrate the data in question 4.2 above. (4)
An octahedron was used as dice in a special edition of snakes and ladders. A player throws the die twice and takes the sum before making a move. Find the mean and variance of the sum of two throws of the die.
Suppose that 3000 randomly breath-tested, 4000 were tested and 98 were above limit
A population consists of the five numbers 2,3,6,8 and 11 consider samples of size 3 that can be drawn from the population
Marks of six students are tabulated below:
Name : Raj Anil Amit Om Rita Renu
Marks : 54 50 52 48 50 52
From the population, tabulated above, you are supposed to choose a sample of size two.
(a) Determine, how many samples of size two are possible
(b) Construct sampling distribution of means by taking samples of size 2 and organize the data.
using continuity correction probability of getting greater than 60 successes
find all possible samples of size 2 which can be drawn without from this population.
Monthly spending ($)
Age
20s
30s
$0.00 - $49.99
75
29
$50.00 - $99.99
91
83
$100.00 - $149.99
113
90
$150.00 - $199.99
89
128
$200.00 - $249.99
63
159
$250.00 or more
34
46
Total customers
465
535
a. What is the probability that a customer spends at least $150.00 or is in his/her 30s?
Monthly spending ($)
Age
20s
30s
$0.00 - $49.99
75
29
$50.00 - $99.99
91
83
$100.00 - $149.99
113
90
$150.00 - $199.99
89
128
$200.00 - $249.99
63
159
$250.00 or more
34
46
Total customers
465
535
a.
b. Are the events “age of 30s” and “monthly spending of $250.00 or more” independent? Explain using probabilities.
