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Sagot :
For the given distribution the mean is 20.74 , the variance is 1.652 and the standard deviation is 1.2853 .
In the question ,
probabilities are given ,
the mean is given by the formula,
mean = [tex]\sum[/tex]x*p(x) ,
we get ,
mean = 19*0.21 + 20*0.23 + 21*0.30 + 22*0.13 + 23*0.13
= 3.99 + 4.6 + 6.3 + 2.86 + 2.99
= 20.74
For calculating the Variance we need to subtract the mean for every value x, then we square the result and multiply it by the respectively probability .
19 - 20.74 = -1.74 = (-1.74)²× 0.21 = 0.6357
20 - 20.74 = -0.74 = (-0.74)²× 0.23 = 0.1259
21 - 20.74 = 0.26 = (0.26)²× 0.30 = 0.0202
22 - 20.74 = 1.26 = (1.26)²× 0.13 = 0.2063
23 - 20.74 = 2.26 = (2.26)²× 0.13 = 0.6639
The variance = 0.6357 + 0.1259 + 0.0202 + 0.2063 + 0.6639
= 1.652
the standard deviation = √variance
= √1.652
= 1.2853
Therefore , the values are mean is 20.74 , the variance is 1.652 and standard deviation is 1.2853 .
Learn more about Standard Deviation here
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