A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 50.0 and 52.
0 minutes. Find the probability that a given class period runs between 51.25 and 51.5 minutes.
1 answer:
Answer: 0.125
Step-by-step explanation:
Given: A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed in interval (50,52).
∴ The probability density function of X will be :-
![f(x)=\dfrac{1}{b-a}=\dfrac{1}{52-50}=\dfrac{1}{2}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdfrac%7B1%7D%7Bb-a%7D%3D%5Cdfrac%7B1%7D%7B52-50%7D%3D%5Cdfrac%7B1%7D%7B2%7D)
The required probability will be:-
![P(51.25](https://tex.z-dn.net/?f=P%2851.25%3Cx%3C51.5%29%3D%5Cint%5E%7B51.5%7D_%7B51.25%7Df%28x%29%5C%20dx%5C%5C%5C%5C%3D%5Cdfrac%7B1%7D%7B2%7D%5Cint%5E%7B51.5%7D_%7B51.25%7D%5C%20dx%5C%5C%5C%5C%3D%5Cdfrac%7B1%7D%7B2%7D%5Bx%5D%5E%7B51.5%7D_%7B51.25%7D%5C%5C%5C%5C%3D%5Cdfrac%7B1%7D%7B2%7D%2851.5-51.25%29%3D%5Cdfrac%7B0.25%7D%7B2%7D%3D0.125)
Hence, the probability that a given class period runs between 51.25 and 51.5 minutes =0.125
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