Answer:
a
[tex]P( X > 46) = 0.7 \ minute[/tex]
b
[tex]\mu = 42 \ minute[/tex]
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
[tex]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.[/tex]
Generally the probability that it takes more than 46 minutes to learn the procedure is mathematically represented as
[tex]P( X > 46) = F(46) = \frac{46 - 32}{52-32}[/tex]
=> [tex]P( X > 46) = 0.7 \ minute[/tex]
Generally the average time required to learn the procedure is mathematically represented as
[tex]\mu = \frac{a + b}{2}[/tex]
=> [tex]\mu = \frac{32 + 52}{2}[/tex]
=> [tex]\mu = 42 \ minute[/tex]
