Question

The data from 200 machined parts are summarized as follows: Depth of Bore Edge Condition Above Target Below Target Coarse 15 10 Moderate 20 25 Smooth 52 78 (a) What is the probability that a part selected has a moderate edge condition and a below-target bore depth? Round your answer to two decimal places (e.g. 98.76).

Answer 1

The probability that a part selected has a moderate edge condition and a below-target bore depth = 0.675.

Step-by-step explanation:

Depth of bore

Edge condition above target below target Total

Coarse 15 10 25

Moderate 25 20 45

Smooth 50 80 130

Total 90 110 200

Let part selected has a moderate edge condition be represented as M, and

part selected has a below target bore depth be represented as B.

P(M or B) = P(M \ B)

= P(M)+P(B)-P(M \ B)

= 45/200+110/200-20/200

= 0.225 + 0.55 - 0.1

=135/200

P(M or B) = 0.675

Thus, the probability that a part selected has a moderate edge condition and a below-target bore depth = 0.675.

Answer 2

The probability that a part selected has a moderate edge condition and a below-target bore depth is 0.13.

Step-by-step explanation:

The given data is as follows:

Edge condition Above target Below target

Coarse 15 10

Moderate 20 25

Smooth 52 78

Total machine parts = 15 + 20 + 52 + 10 + 25 + 78

= 200

In general, Probability = Possible outcomes / Total outcomes

Probability that a part selected has a moderate edge condition and a below-target bore depth

= 25 / 200

= 0.125

= 0.13 (rounded to two decimal places)