maths statistics paper

A coach recorded the heights of some adult rugby players and found the following summary statistics.

Median = 1.85 m

Range = 0.28 m

Interquartile range = 0.11 m

The coach also noticed that

• the height of the shortest player is 1.72 m

• 25% of the players' heights are below the height of a player whose height is 1.81 m

Draw a box and whisker plot to represent this information on the grid below.

from , Q1 = 1.81

IQR= 0.11

IQR: Q3-Q,

Q3 - 1.81 = 0.11

Q3 = 1.92

Range = highest value-lowest value

0.28=highest value-1.72

highest value: 0.28+1.72=2.0

Using your knowledge of the large data set state, giving a reason, which direction

A represents.

A represents East, since the prevailing winds in Camborne are from the south, North or West.

State, giving a reason, what Keith should do with this value.

Wind direction should be within the range O to 360, so the value should be ignored

Complete the table.

3 - 4: frequency = 13, class width (cw) = 1

frequency density (fd) = 13/1 =13

2-3 frequency: 25 x 1 = 25

Complete the histogram.

1-2: freq = 64, cw= 1, fd = 64.

4 - 6: freq = 7, cw = 2, fd = 7/2 =3.5

6-8: freq = 3, cw= 2, fd = 3/2 =1.5

Find the value of k

128

The random variable X ~ B(27, 0.35)

(a) Find

(i) P(X= 10)

(il) P(12 < X < 15)

Historical records show that the proportion of defective items produced by a machine is 0.12

Following a maintenance service of the machine, a random sample of 60 items is taken and 3 defective items are found.

(b) Carry out a suitable test to determine whether the proportion of defective items produced by the machine has decreased following the maintenance service.

You should state your hypotheses clearly and use a 5% level of significance.

(c) Write down the p-value for your test in part (b)

Find the value of q

0.5 + 0.2 + q + q = 1

2q = 0.3

q =0.15

Show that the probability that Karen stops after taking her 3rd spin is 0.128

P( stops after 3rd spin) = not 7 x not 7 x yes 7

= 0.8 × 0.8 x0.2

= 0.128

Find the probability distribution for S part 1

Find the probability distribution for S part 2

Find P(S > N)