given a normal distribution with u 47 and s 3 a what the pro

given a normal distribution with u =47 and s =3

a) what the probability that x > 42 ?

b) what the probability that x < 41?

c) for this distribution 9% the value are less than what x value ?

d) between what two x values (symmetrically distributed around the mean) are 80% of values ? for this distribution 80% of the values are between x= ( ) and x= ( )

Solution

a) what the probability that x > 42 ?

P(X>42) = P((X-mean)/s >(42-47)/3)

=P(Z>-1.67) =0.9525 (from standard normal table)

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b) what the probability that x < 41?

P(X<41) = P(Z<(41-47)/3)

=P(Z<-2) =0.0228 (from standard normal table)

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c) for this distribution 9% the value are less than what x value ?

P(X<x)=0.09

--> P(Z<(x-47)/3)=0.09

--> (x-47)/3 = -1.34(from standard normal table)

So x= 47-1.34*3=42.98

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d) between what two x values (symmetrically distributed around the mean) are 80% of values ? for this distribution 80% of the values are between x= ( ) and x= ( )

Given a=1-0.8=0.2, Z(0.1)=1.28 (from standard normal table)

So mean- 1.28*s=47-1.28*3 =43.16

So mean +1.28*s=47+1.28*3=50.84