Reference no: EM132606667

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

Show these data in a stem and leave diagram.

Calculate the mean

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 0 5 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)
9 0 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 27 28 28 28 29 29 2930 32
32 32 34 34 35 35 35 35 36 37 38 38 44 45 48
Calculate;
The median
The 3rd decile
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    

Code the data by using T= ( t-12.5)/5

Calculate estimates of the mean and variance of the coded data

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'

Find the probabilities:
P(G)
ii) P (G∩D)
P(D|G)

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    

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.

Find μ

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 pairs of values (c, r) of the variables gave the following results:
Σc=58, Σr =51, Σc² = 530, Σr²=379.76, Σcr=402.7

Find the values of μ_c , μ_r , S_cr, S_cc

Find the equation of the regression line of r on c