Question

If ? has N (60, 4), find: a. P(X ≤ 68) b. P(54<X<68) c. P(X >...

If ? has N (60, 4), find:

a. P(X ≤ 68)
b. P(54<X<68)
c. P(X > 68)
d. ThevalueofcsuchthatP(X ≤ c)=0.06

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Answer #1

Solution-A:

P(X<=68)

P(Z<=68-60/4)

P(Z<=2)

=0.9772

0.9772

Solution-B:

P(54<X<68)

=P(54-60/4<Z<68-60/4)

=P(-1.5<Z<2)

P(Z<2)-P(Z<-1.5)

=0.9772-(1-P(Z<1.5))

=0.9772-(1-0.9332)

=0.9772-(0.0668)

=0.9104

Solution-c:

P(X>68)

=1-P(X<68)

=1-P(Z<2)

=1-0.9772

=0.0228

Soluti0n-c:

P(X<c)=0.06

c=-1.55

d. ThevalueofcsuchthatP(X ≤ c)=0.06

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