Practice Paper Statistics 1 (Edexcel International AS Maths: Mechanics 1)

Practice Paper Questions

1a
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4 marks

A bag contains 12 red marbles, 7 green marbles and 1 black marble. Two marbles are drawn from the bag without replacement.

Draw a tree diagram to represent this experiment.

1b
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3 marks

Find the probability that the two marbles drawn are not both the same colour.

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2a
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5 marks

 Three events,A, B and C, are such that Aand B are independent Band C and  are mutually exclusive. straight P open parentheses C close parentheses equals 0.55P open parentheses open parentheses A intersection B close parentheses union open parentheses A intersection C close parentheses close parentheses equals 0.07, and the following two relations also hold: 

8 space straight P open parentheses A close parentheses equals 25 space straight P open parentheses B close parentheses

straight P open parentheses A to the power of apostrophe intersection C close parentheses equals 10 space straight P open parentheses A intersection C close parentheses

Using the above information, draw a Venn diagram to show the probabilities for events A,B and C.

2b
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3 marks

Find:

(i)
straight P open parentheses C vertical line A close parentheses

(ii)
straight P open parentheses B vertical line A to the power of apostrophe close parentheses

(iii)
straight P open parentheses open parentheses A union B union C close parentheses to the power of apostrophe vertical line open parentheses A union B close parentheses to the power of apostrophe close parentheses

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3a
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5 marks

The histogram below shows the masses, in grams, of 80 apples.

q3a-1-2-hard-ial-sl-maths-statistics

Find estimates for the median, lower quartile and upper quartile.

3b
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2 marks

Given that the lightest apple weighs 41 g and that the range of masses is 97 g, draw a box plot to show the distribution of the masses of the apples.

q3b-1-2-hard-ial-sl-maths-statistics

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4a
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3 marks

The ages, x years, of 200 people attending a vaccination clinic in one day are summarised by the following:  straight capital sigma x= 7211  and  straight capital sigma x squared= 275 360.

Calculate the mean and standard deviation of the ages of the people attending the clinic that day.

4b
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4 marks

One person chooses not to get the vaccine, so their data is discounted. The new mean is exactly 36.  Calculate the age of the person who left and the standard deviation of the remaining people.

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5a
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6 marks

The masses of turkeys can be modelled using a normal distribution with a mean of 4.7 kg and a variance of 1.9 kg².  Nicholas, a farmer, classes a turkey as ‘holiday ready’ if it weighs more than 5.5 kg.

A turkey is selected at random. Given that it is ‘holiday ready’, find the probability that it weighs less than 6 kg.

5b
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5 marks

Nicholas takes a large sample of ‘holiday ready’ turkeys, estimate the median mass of the turkeys in his sample.

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6a
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5 marks

A machine is used to fill bags of potatoes for a supermarket chain. The weight, W kg, of potatoes in the bags is normally distributed with mean 3 kg and standard deviation sigma kg. 

Given that 7% of the bags contain a weight of potatoes that is at least 50 g more than the mean, find:

P left parenthesis 2.9 less or equal than W less or equal than 3.1 right parenthesis.

6b
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4 marks

Two of the bags of potatoes are chosen at random.

Find the probability that neither of the bags will contain less than 2.96 kg of potatoes.

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7a
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6 marks

A discrete random variable, X, can take the values 1, 3, 5 or 7 and it has the cumulative distribution function straight F open parentheses x close parentheses given in the table.

x

1

3

5

7

straight F open parentheses x close parentheses

0.5

0.65

0.9

1

Find the value of:

(i)
P left parenthesis X equals 3 right parenthesis
(ii)
P left parenthesis 3 X plus 3 greater than X plus 9 right parenthesis
(iii)
E left parenthesis X right parenthesis
(iv)
text Var end text left parenthesis X right parenthesis.
7b
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5 marks

Find the value of:

(i)
E open parentheses X over 2 plus 7 close parentheses

(ii)
Var open parentheses fraction numerator 2 minus straight x over denominator 5 end fraction close parentheses

(iii)
E left parenthesis 3 X squared minus 1 right parenthesis.

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8
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4 marks

The random variable X has the probability function

straight P open parentheses X equals x close parentheses equals open curly brackets table row cell 1 over k end cell cell x equals 1 comma 2 comma 3 comma 4 comma 5 comma 6 space end cell row 0 cell otherwise. end cell end table close

(i)
Write down the value of k.
(ii)
Write down the name of this probability distribution.
(iii)
Find the values of straight E left parenthesis X right parenthesis and Var left parenthesis X right parenthesis.

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9a
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6 marks

Charlie is interested to find out if there is positive correlation between the number of letters in someone’s name, l, and the time, t rounded to the nearest five seconds, it takes her six-year-old sister to correctly guess the spelling of the name.  She decides to test this by looking at a random sample of different names and timing how long it takes her sister to guess their spelling.

Letters, bold italic l

 4  5  5  5  6  7

Time, bold italic t

 10  5  15  25  60  80

Frequency

 x  3  29  17  7  1

Given that S subscript u equals 17.9375, find the value of x and hence find the number of names in Charlie’s sample.

9b
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5 marks

Charlie calculates the equation of the regression line of t on l to be space t equals 25.9146 l minus 107.8049 and the product moment correlation coefficient to be 0.84428 correct to 5 decimal places.

(i)
Find the value of S subscript l t end subscript and S subscript t t end subscript each to 5 significant figures. 
(ii)
Explain why Charlie should not use this equation to estimate the number of letters that are in someone’s name if it took her sister 70 seconds to guess the spelling.

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