## Primary School

1.   Pocket money, adduced in a simple survey of class 2, produced these results in pennies:

0, 5, 5, 6, 6,10,10, 10,15, 15,15, 15,15, 20, 20, 20, 20, 25,25, 50

i)  Construct a stem and leaf diagram in 5p units, 0-5, 6-10 and so on... [3]

ii)  Comment on the distribution                                                                  [3]

iii)  Construct a box and whisker plot, and                                                  [4]

iv) Find the standard deviation and comment on any outliers                      [4]

2.  Danielle is playing with coloured bricks; she has a box containing 30 red, 20 yellow and 10 blue bricks. If she closes her eyes before selecting bricks, calculate the probability (use reduced fractions or 4s.f.) that she picks:

i)  two blue

ii)  three different

iii)  three of the same colour                                                             [1,2,2]

In the cupboard is a big box containing a lot more blocks with colours in the same proportions. If she picks from this collection in the same way, what is the probability now that she chooses

iv)  three different

v)  two different

vi)  a red before a yellow                                                               [2,4,5]

3. Paul has a set of twenty cards with words on. No words are the same and the cards are either blue or yellow. In how many ways can he pick

i) four cards,                                                                                                      [2]

ii) four cards, given that two of the four have the words POOR and POUR     [2]

POOR and POUR are on cards of different colours. There are twelve blue cards.

iii) Show that the number of ways Paul can pick two cards of each colour is 1848

iv) Find how many of these ways include POOR and POUR                         [2,2]

v) Show the complete distribution of the two colours in picking four cards from the set of twenty and show that your total is correct.                                                                 [4]

vi) What is the probability of picking two cards of each colour given that POOR and POUR are included?                                                                                                         [3]

4.  Class 1 has 20 children, who have difficulty putting their wellingtons on the correct feet. If you assume they guess, then, giving suitable detail,

i) how many would you expect to ‘boot’ correctly? Any more assumptions here?              [3]

ii)  What is the probability that, on any one occasion, more than half the class succeed and hence,                                                                                                                                    [2]

iii)  Find the range of numbers you would accept in support of these assumptions             [3]

iv)  Give the probability that more than half succeed for a whole week (once a day for five days). What does this imply for a whole year of 40 weeks?                                                             [3]

v)  How does this result affect your initial assumption? How many successes every day would you accept before changing your mind?                                                                               [4]

[60]

Danielle joined the Army. Paul became a Civil Engineer. Class 1 learned eventually. The worst grade at S1 was a B.

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