Question

Suppose the time it takes a student to finish a quiz is uniformly distributed between six and 22 minutes, inclusive.

1) Find the value of a=  

 2) Find the value of b=  

3) Find the value of h =    4 d.p.

4) Find the mean time to fix the furnance =       up to 2 d.p.

5) Find the standard deviation time to fix the furnance =    up to 2 d.p.

6) Find the probability  P( x ≤ 19)  =   in %

Answer 1

$1: a=6\\2: b=22\\3: h=22-6=16\\4: EX=\frac{a+b}{2}=\frac{6+22}{2}=14\\5: \sigma X=\frac{b-a}{2\sqrt{3}}=\frac{22-6}{2\sqrt{3}}=4.6188\\6: P\left( X\leqslant 19 \right) =\frac{19-a}{h}=\frac{19-6}{16}=0.8125$