QUESTION IMAGE
Question
the graph to the right is the uniform probability density function for a friend who is x minutes late. (a) find the probability that the friend is between 25 and 30 minutes late. (b) there is a 50% probability the friend will arrive within how many minutes? (a) the probability that the friend is between 25 and 30 minutes late is □. (type an integer or a decimal. round to three decimal places as needed.) (b) there is a 50% probability the friend will arrive within □ minutes. (type a whole number.)
Step1: Calculate probability for part (a)
For a uniform distribution \( f(x)=\frac{1}{b - a}\), here \(a = 0\), \(b=30\). The probability \(P(c<X<d)=\frac{d - c}{b - a}\). For \(c = 25\), \(d = 30\), we have \(P(25<X<30)=\frac{30 - 25}{30-0}\).
Step2: Calculate time for part (b)
Let the time be \(t\). We know that \(P(0<X<t)=0.5\). Using the formula \(P(0<X<t)=\frac{t - 0}{30-0}\). Set \(\frac{t}{30}=0.5\). Solving for \(t\), we get \(t=0.5\times30\).
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(a) \(0.167\)
(b) \(15\)