Answer: The probability that a given class period runs between 51.25 and 51.5 minutes is 0.025.
The probability of selecting a class that runs between 51.25 and 51.5 minutes is 0.025.
Step-by-step explanation:
Probability distribution function for uniformly distributed variable x in [a,b] in interval : [tex]f(x)=\dfrac{1}{b-a}[/tex]
It is given that , 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 lengths of her classes.
Then , the probability distribution function for X will be :
[tex]f(x)=\dfrac{1}{56-46}=0.10[/tex]
Then, the probability that a given class period runs between 51.25 and 51.5 minutes will be :
[tex]\int^{51.5}_{51.25}f(x)\ dx=0.1\int^{51.5}_{51.25}\ dx\\\\= 0.10[x]^{51.5}_{51.25}\\\\=0.10[51.5-51.25]=0.025[/tex]
Hence, probability that a given class period runs between 51.25 and 51.5 minutes is 0.025.
It is same for the probability of selecting a class that runs between 51.25 and 51.5 minutes.
