The Time X (Minutes) for a Lab Assistant to Prepare

Question

Examlex · Accepted Answer

The Answer is a.

f ( x ) = \frac { 1 } { 10 } ext { for } 20 \leq x \leq 30 ext { and } = 0 ext { otherwise }

b.

P ( X > 27 ) = \int _ { 27 } ^ { 30 } \frac { 1 } { 10 } d x = .3

c.

\left. E ( X ) = \int _ { 20 } ^ { 30 } x \cdot \frac { 1 } { 10 } d x = \frac { x ^ { 2 } } { 20 } ight] _ { 20 } ^ { 30 } = 25

25

\pm

2 is from 23 to 27 minutes:

\left. P ( 23 < x < 27 ) = \int _ { 23 } ^ { 27 } \frac { 1 } { 10 } d x = \frac { x } { 10 } ight] _ { 23 } ^ { 27 } = .40

d.

P ( a \leq x \leq a + 2 ) = \int _ { a } ^ { a + 2 } \frac { 1 } { 10 } d x = .2

since the interval has length 2.

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