Answer:
0.025
Step-by-step explanation:
Given that a statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 46.0 and 56.0 minutes
Let X be the length of the class of statistics professor
X is U(46,56)
We are to find the probability that a given class period runs between 51.25 and 51.5 minutes.
The pdf of X is = [tex]\frac{1}{56-46} =0.1, 46\leq x\leq 56[/tex]
Using this we can find probability using integration
[tex]P(51.25\leq x\leq 51.5)[/tex]
=[tex]\int\limits^{51.5} _{51.25} 0.1 \, dx \\=0.1(51.5-51.25)\\= 0.025[/tex]
