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SUMMER-2022-STA2023-6-PickHomework: HmWrk-16-1< Question 6, 6.1.8 >HW Score: 5.97%, 12 of 201 pointsPoints: 0 of 10SaveA 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 period runsbetween 50.75 and 51.25 minutes.Find the probability of selecting a class that runs between 50.75 and 51.25 minutes.(Round to three decimal places as needed.)Clear allCheck answerTextbook StatcrunchMacBook ProWidline Jules

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Answer:

The probability that a given class period runs between 50.75 and 51.25 minutes is 0.05

The probability of selecting a class that runs between 50.75 and 51.25 minutes is 0.05

First, we need to find the probability density of the given variables. Since the distribution runs from 46.0 to 56.0, we have a range of 10.0. To make it 1, we will have to divide 1 by 10 resulting in 0.1.

Now that we have the probability density, we will subtract the given range from each other, then multiply the result by the probability density to find the probability that a given class period runs between 50.75 and 51.25 minutes:

[tex]0.1(51.25-50.75)=0.05[/tex]

To find the probability of selecting a class that runs between 50.75 and 51.25 minutes:

[tex]\begin{gathered} P(A)=\frac{51.25-50.75}{56-46} \\ P(A)=0.05 \end{gathered}[/tex]

Therefore:

The probability that a given class period runs between 50.75 and 51.25 minutes is 0.05, while the probability of selecting a class that runs between 50.75 and 51.25 minutes is 0.05 as well.

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