Question

The time (in minutes) required to learn the procedure for performing a certain task is uniformly distributed on the interval from 32 minutes to 52 minutes. (a) What is the probability that it takes more than 46 minutes to learn the procedure?(b) What is average time reqiured to learn the procedure?

Answer 1

a

`P( X > 46) = 0.7 \ minute`

b

`\mu = 42 \ minute`

Explanation:

From the question we are told that

The procedure for performing a certain task is uniformly distributed on the interval from( a = 32 )minutes to (b= 52) minutes

Generally the cumulative distribution function for continuous uniform distribution is

`F(x) = \left \{ {{0 \ \ \ \ \ for \ x \ x < a} \atop {(x-a)/(b-a) } \ \ for \ a \le x \ge b} \atop {1 \ \ \ \ \ \ \ for \ x > b }\right.`

Generally the probability that it takes more than 46 minutes to learn the procedure is mathematically represented as

`P( X > 46) = F(46) = (46 - 32)/(52-32)`

=>
`P( X > 46) = 0.7 \ minute`

Generally the average time required to learn the procedure is mathematically represented as

`\mu = (a + b)/(2)`

=>
`\mu = (32 + 52)/(2)`

=>
`\mu = 42 \ minute`