Answer: The probability that a given class period runs between 51.5 and 51.75 minutes = 0.025
The probability of selecting a class that runs between 51.5 and 51.75 minutes = 0.025
Step-by-step explanation:
The probability density function for random variable x uniformly distributed in [a,b] is given by:-
[tex]f(x)=\dfrac{1}{b-a}[/tex]
Given : A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 46.0 and 56.0 minutes. Find the probability that a given class
Let x be the lengths of her classes.
[tex]f(x)=\dfrac{1}{56-46}=\dfrac{1}{10}=0.1[/tex]
Then, the probability that a given class period runs between 51.5 and 51.75 minutes will be :-
[tex]P(51.5<X<51.75)=\int^{51.75}_{51.5 }f(x)\ dx\\\\= \int^{51.75}_{51.5 }(0.1)\ dx\\\\=(0.1)[x]^{51.75}_{51.5 }\\\\=(0.1)(51.75-51.5)=0.025[/tex]
Hence, the probability that a given class period runs between 51.5 and 51.75 minutes = 0.025
The probability of selecting a class that runs between 51.5 and 51.75 minutes = 0.025
Using the uniform distribution, it is found that there is a 0.025 = 2.5% probability of selecting a class that runs between 51.5 and 51.75 minutes.
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An uniform distribution has two bounds, a and b.
The probability of finding a value between c and d is:
[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 46.0 and 56.0 minutes, thus the parameters are [tex]a = 46, b = 56[/tex]
Find the probability that a given class period runs between 51.5 and 51.75 minutes:
[tex]P(51.5 \leq X \leq 51.75) = \frac{51.75 - 51.5}{56 - 46} = 0.025[/tex]
0.025 = 2.5% probability of selecting a class that runs between 51.5 and 51.75 minutes.
A similar problem is given at https://brainly.com/question/24746255
