Question

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 all

Answer 1

ANSWER

$0.050$

EXPLANATION

In the uniform distribution given above, the lower limit is 46 and the upper limit is 56.

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

Recall;

$P(50.75Substitute the values;[tex]\begin{gathered} a=46 \\ b=56 \\ c=50.75 \\ d=51.25 \\ P(50.75\lt x\lt51.25)=\frac{d-c}{b-a} \\ \frac{51.25-50.75}{56-46} \\ =\frac{0.5}{10} \\ =0.05 \end{gathered}$

Hence, the probability that a given class period runs between 50.75 and 51.25 minutes is 0.050