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Anni [7]
3 years ago
11

The time (in minutes) required to learn the procedure for performing a certain task is uniformly distributed on the interval fro

m 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?
Mathematics
1 answer:
PtichkaEL [24]3 years ago
3 0

Answer:

a

 P( X >  46)  = 0.7 \  minute

b

\mu  = 42 \ minute

Step-by-step 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 {\frac{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) = \frac{46 - 32}{52-32}

=>       P( X >  46)  = 0.7 \  minute

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

        \mu =  \frac{a + b}{2}

=>     \mu  =  \frac{32 + 52}{2}

=>     \mu  = 42 \ minute

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A certain plant runs three shifts per day. Of all the items produced by the plant, 50% of them are produced on the first shift,
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We use the conditional probability formula to solve this question. It is

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P(B|A) is the probability of event B happening, given that A happened.

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