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Conditional probabilities with normal intervals

DIFFICULTYintrostandardchallengeexam
QUESTION TYPEMix of allChange
A given B with a contained intervalB given A with a contained intervalA given B with overlapping intervalsB given A with overlapping intervalsA given B with disjoint intervalsNOWMix of allRecommended
Question 1 of 8

Calculator allowed

The normal model for X is given below

Let X be the length, in millimetres, of a manufactured component

The distribution is \(X\sim N\left(54,9\right)\)

Event \(A\) is \(45<X<63\)

Event \(B\) is \(48<X<63\)

The required conditional probability is \(\Pr(B\mid A)\)

(a)1 mark

Select the interval containing values that satisfy both events

(b)1 mark

Find the probability for the event after the vertical bar

Format: 4 d.p.
(c)1 mark

Calculate the probability for values satisfying both events

Format: 4 d.p.
(d)1 mark

Find the conditional probability for the displayed events

Format: 4 d.p.