Reference no: EM132710410
QUESTION ONE
A group of year 12 students recorded their pulse rate when they were in a relaxed state.
67 62 58 75 62 79 63 55 71 64 69 57
64 59 73 62 69 63 68 55 83 59 62 67
80 71 67 63 65 59 70 62 65 68 54 67
a) Show these data in a stem and leave diagram.
b) Calculate the mean
c) Calculate the variance hence the standard deviation
QUESTION TWO
Old faithful is a geyser in yellow stone National park in the USA. The times (in minutes, to the nearest minute) between eruptions are recorded and displayed in a stem and leaf diagram below.
4 8 (1)
5 0 0 4 4 5 6 7 7 8 8 (10)
6 0 05 5 8 (5)
7 1 3 4 5 5 6 6 7 8 9 (10)
8 0 1 2 3 4 5 5 6 7 8 9 (11)
90 1 3 (3)
Key: 6|5 means an interval of 65 minutes between eruptions. Find the median and quartiles of these times.
QUESTION THREE
A group of 45 women go on a skiing holiday. Their ages are listed below.
17 17 17 19 1919 20 22 22 22 23 23 24 25 25
25 26 26 26 26 27 2728 28 28 29 29 2930 32
32 32 34 34 35 35 35 35 36 37 38 38 44 45 48
Calculate;
a) The median
b) The 3rddecile
c) The 19th percentile of these pulse rates
QUESTION FOUR
The table below shows the information about the daily times spent with patients by a nurse in a care home during one month.
|
Time,t (minutes)
|
frequency
|
|
10< t ≤15
|
312
|
|
15< t ≤ 20
|
479
|
|
20 < t ≤ 25
|
243
|
|
25 < t ≤ 30
|
119
|
a) Code the data by using T= ( t-12.5)/5
b) Calculate estimates of the mean and variance of the coded data
c) Use your answers to part (b) to give estimates of the mean and variance of the time spent with a patient
QUESTION FIVE
Over the course of a season, a hockey team play 40 matches, in different conditions, with the following results.
|
|
Good
|
Bad
|
Total
|
|
Win
|
13
|
6
|
19
|
|
Draw
|
5
|
3
|
8
|
|
Lose
|
7
|
6
|
13
|
|
Total
|
25
|
15
|
40
|
For a match chosen at random from the season:
G is the event ‘Good weather'
W is the event ‘Team wins'
D is the event ‘Team draws'
L is the event ‘Team loses'
a) Find the probabilities:
i) P(G)
ii) P (G∩D)
iii) P(D|G)
b) Are the events D and G independent?
QUESTION SIX
Here is a set of bivariate data
|
X
|
3.5
|
4.8
|
4.9
|
7.2
|
8.5
|
8.8
|
9.3
|
10.4
|
10.8
|
11
|
|
Y
|
0.9
|
10.9
|
2.3
|
0.6
|
10.9
|
7.4
|
7.1
|
10.4
|
6.5
|
2.4
|
a) Use it to calculate the regression line of X on Y
Calculate the correlation coefficient between X and Y and comment on its value
QUESTION SEVEN
The 30 members of the Darton town orchestra each recorded the mount of individual practice, x hours; they did in the first week of June. The results were summarized as follows:
Σx =225 Σx2 =1755
The mean and standard deviation of the number of hours of practice undertaken by the members of Darton Orchestra in this week were μ and w respectively.
a) Find μ
b) Find w
Two new people joined the Orchestra and the number of hours of individual practice they did in the first week of June were μ-2w and μ+2w
State giving reasons whether the effect of including these two Members increases, decreases; or leaves unchanged the mean and the standard deviation.
QUESTION EIGHT
The variables C and R are known to be approximately linearly related. Seven pairsof values (c, r) of the variables gave the following results:
Σc=58, Σr =51, Σc2= 530, Σr2=379.76, Σcr=402.7
a) Find the values of μc , μr ,Scr, Scc
b) Find the equation of the regression line of r on c