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STATISTICS1

Practice Paper1TIME: 1 HOUR MARKS: 75 26/02/14

Name : K.Praveen Kumar Class : Grade - 11

1. (a) Find the first 3 terms in ascending powers of x of giving each term

in its simplest form. [4]

(b)The coefficient of in the binomial expansion of ( ),whereis a positive integer, are 15 and 90.show that value of is 5 and find the value of [6]

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2. (a)A model predicts that a culture of bacteria doubles every hour.

If there are 500 bacteria at the beginning,

(i) How many bacteria will there be after 12 hours? [3]

The model predicts that after N hours the total population of bacteria will exceed 10 million.

(ii) Find the value of N. [4]

(b) The sum to infinity of the terms in the sequence below is 2.

Find the value of [3]

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3. The events A, B and C are defined as in the below Venn diagram.

Use the diagram to find the following probabilities:

(a) ( ) [2](b)

(|) [3]

(c) ( ) [1](d) ( ) [2]---------------------------------------------------------------------------------------------------------------------

4. I have three 2-laari coins and two 10-laari coins in my pocket. I pick two coins out of my pocket

at random. Find the probability that they are

(a) Draw a tree diagram to represent this information. [3]

(a)Both 10laari coins [1](b)Both of the same value [3](c)Find the probability that the coins are both the same, given that the first coin was a 2-laari coin.

[1]

(d)Find the probability that the first coin was a 2-laari coin given that the coins were both the same. [3]

The event T is that the sum of the two coins values is 20 laari and the event S is that the two

coins are the same.

(e)Find (|) [2](f) State, with a reason, whether or not event S and T are independent. [2]

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5. In a shopping survey a random sample of 160 females were asked how many hours, to

the nearest hour, they spent shopping in the last month. The results are summarized in

the table below.

A histogram was drawn and the group (02) hours

was represented by a rectangle that

was 0.5 cm wide and 4 cm high.

(a) Calculate the width and height of the rectangle representing the group (68). [4]

(b) Use linear interpolation to estimate the median and interquartile range. [5]

(c) Estimate the mean and the standard deviation of the number of hours spent shopping. [4]

(d) State, giving a reason, which average and measure of dispersion you, would

recommend to use to summarise these data. [2]

One measure of skewness is( )

(e) Use this measure to calculate the skewness for these data and describe its value. [2]

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Number of hours Frequency

02 50

35 25

68 18

912 16

1317 20

1825 31

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6 . A firm of accountants recorded the time, minutes, to the nearest minute, taken to check theaccounts of their clients. The values of are illustrated in the stem leaf diagram below.

For these data:

(a) Find the median and Interquartile range. [4]

A value that is greater than ( ) or smaller than ( )isdefined as an outlier.

(b) Find the outliers. [2]

(c) Using the graph paper draw a box plot for these data. [5]

(d) Using your anwsers for part(a), State the skewness and justify your answer. [2](e) Write down which of the mean and median you would prefer to use a representation

for these data. Justify your choice. [2]

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