Question

1. Find the standard variation of the following data. Round your answer to one decimal place.

2. find the value of P( X > 3)

3. find the value of P (X [less than or equal to] 7)

x	3	4	5	6	7
P(X=x)P(X=x)	0.2	0.2	0.1	0.2	0.3

Answer 1

SOLUTION:

From given data,

1. Find the standard variation of the following data. Round your answer to one decimal place.

Mean = = x * P(x)

E(X) = = (3*0.2)+(4*0.2)+(5*0.1)+(6*0.2)+(7*0.3)

E(X) = 0.6+0.8+0.5+1.2+2.1

E(X) = 5.2

Variance = x ²* P(x) = (3²*0.2)+(4²*0.2)+(5²*0.1)+(6²*0.2)+(7²*0.3)

Variance = 1.8+3.2+2.5+7.2+14.7 = 29.4

Standard deviation = = sqrt(Variance ) = sqrt(29.4) = 5.4

Standard deviation =5.4

2. find the value of P( X > 3)

P( X> 3) = P(X=4) +P(X=5)+P(X=6) +P(X=7)

P( X > 3) =0.2 +0.1+0.2 +0.3

P( X > 3) =0.8

3. find the value of P (X [less than or equal to] 7)

P(X < 7) = P(X=3)+P(X=4) +P(X=5)+P(X=6) +P(X=7)

P(X < 7) = 0.2+0.2+0.1+0.2+0.3

P(X < 7) = 1