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swat32
3 years ago
11

A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 48.0 and 58.

0 minutes. Find the probability that a given class period runs between 50.25 and 50.5 minutes. Find the probability of selecting a class that runs between 50.25 and 50.5 minutes.
Mathematics
1 answer:
Yanka [14]3 years ago
5 0

Answer: 0.025

Step-by-step explanation:

Given : A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between the interval [48.0 minutes, 58.0 minutes].

The probability density function :-

f(x)=\dfrac{1}{58-48}=\dfrac{1}{10}

Now, the probability that a given class period runs between 50.25 and 50.5 minutes is given by :-

\int^{50.5}_{50.25}\ f(x)\ dx\\\\=\int^{50.5}_{50.25}\ \dfrac{1}{10}\ dx\\\\=\dfrac{1}{10}|x|^{50.5}_{50.25}\\\\=\dfrac{1}{10}\ [50.5-50.25]=\dfrac{1}{10}\times(0.25)=0.025

Hence, the probability that a given class period runs between 50.25 and 50.5 minutes =0.025

Similarly , the probability of selecting a class that runs between 50.25 and 50.5 minutes = 0.025

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