Question

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 period runs between 51.5 and 51.75 minutes. find the probability of selecting a class that runs between 51.5 and 51.75 minutes. (round to three decimal places as needed.)

Explanation:

Step1: Determine the formula for uniform distribution probability

For a uniform distribution \(U(a,b)\), the probability density function \(f(x)=\frac{1}{b - a}\), and the probability \(P(c<X<d)=\frac{d - c}{b - a}\), where \(a = 46.0\), \(b = 56.0\), \(c = 51.5\), \(d = 51.75\).

Step2: Calculate \(b - a\)

\(b - a=56.0 - 46.0 = 10\)

Step3: Calculate \(d - c\)

\(d - c=51.75 - 51.5=0.25\)

Step4: Calculate the probability

\(P(51.5<X<51.75)=\frac{0.25}{10}=0.025\)

Answer:

\(0.025\)