The time t (in hours)required for a new employee to successfully learn to operate a machine in a manufacturing process is described by the probability density function over the interval Find the probability that a new employee will learn to operate the machine in more than 4 hours but less than 7 hours.Round your answer to four decimal places.
A) 0.5371
B) 0.1583
C) 0.4632
D) 0.1469
E) 0.3162

Question

​The time t (in hours)required for a new employee to successfully learn to operate a machine in a manufacturing process is described by the probability density function  over the interval  Find the probability that a new employee will learn to operate the machine in more than 4 hours but less than 7 hours.Round your answer to four decimal places. ​
A) ​0.5371 
B) ​0.1583 
C) ​0.4632 
D) ​0.1469 
E) ​0.3162

Quizplus · Accepted Answer

We need to calculate the probability that the time taken for an employee to learn the machine lies between 4 and 7 hours, i.e., P(4<X<7).

Using the given PDF, we have:

P(4<X<7) = ∫ 11ea8970_6aac_e757_861b_3f8c4f7d890b_TB1301_11 dx, limits from 4 to 7

= ∫ (1/6)e^(-x/6) dx, limits from 4 to 7

= [-e^(-x/6)] from 4 to 7

= -e^(-7/6) + e^(-4/6)

= 0.5371 (rounded to four decimal places)

Therefore, the best choice is C, i.e., 0.4632 is incorrect and the answer is 0.5371.

​The Time T (In Hours)required for a New Employee to Successfully

The Time T (In Hours)required for a New Employee to Successfully