Qualification > Math
statistics n09
sweetie:
hey ppl,
can sum1 plzzz xplain q1 of paper6 ( statistics) second variant?????/
Thank You
Freaked12:
which year?
Chingoo:
First of all, identify the possible outcomes (i.e. possible sums of the numbers on the dice). These will be 16 in number ('4 sides of dice x 2' as there are 2 dice). If you want (though it's not needed), a possibility diagram can be drawn.
1|2 3 4 5
2|3 4 5 6
3|4 5 6 7
4|5 6 7 8
-------
1 2 3 4
Hence, the probability of scoring a sum more then or equal to 7 is 3/16. As you can see, it is a binomial distribution, because the probability 'p' (probability of success, as in this case the probability of scoring a sum more then or equal to 7 is 3/16) remains constant with each throw i.e. the probability is independent. The experiment is also being repeated several times. For this,
E(X)=np i.e. Expected Value=(Number of trials)(Probability of success)
therefore, for this distribution E(X)=(200)(3/16)
=37.5
sweetie:
I guess u xplained the wrong que., but anywayz thanx :)
its no09 q1 2nd variant
Chingoo:
Okay. :)
If you notice the box-and-whisker plot is normally distributed i.e. the mid-point of the interquartile range is the median, and the distribution extends to equal length on either side. Hence, for part (a), the mid-point is the mean, just like in the normal distribution curve, the line of symmetry passes through the mean. i.e. (63+39)/2 = 51.
In the second part, the examiner wants the standard deviation. You have the mean, two values of x and z which can be found by keeping the fact that P(x<=63)=P(x>=39)=0.75. Remember, the quartiles divide the distribution into four parts, such that the Q1 is the lower 1/4th of the distribution, while the Q3 is the 1 - upper 3/4th of the distribution. Meaning thereby, that the probability of x being more than or equal to the Q1 is 0.75, and less than or equal to Q3 is also 0.75. So, z = +0.674 or -0.674. Now just insert these values into the formula:
z = (x - mu)/sigma
Remember, z = -0.674 for x=63, and vice versa. You can use either of the two sets of values.
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