Question

the time it takes me to wash the dishes is uniformly distributed between 9 minutes and 19 minutes. what is the probability that washing dishes tonight will take me between 17 and 18 minutes? give your answer accurate to two decimal places.

Explanation:

Step1: Recall Uniform Distribution Probability Formula

For a uniform distribution between \(a\) and \(b\), the probability density function is \(f(x)=\frac{1}{b - a}\) for \(a\leq x\leq b\), and the probability of \(X\) being between \(c\) and \(d\) (where \(a\leq c\leq d\leq b\)) is \(P(c\leq X\leq d)=\frac{d - c}{b - a}\).
Here, \(a = 9\), \(b = 19\), \(c = 17\), \(d = 18\).

Step2: Calculate the Probability

Substitute the values into the formula: \(P(17\leq X\leq 18)=\frac{18 - 17}{19 - 9}\).
First, calculate the numerator: \(18 - 17 = 1\).
Then, calculate the denominator: \(19 - 9 = 10\).
So, \(P(17\leq X\leq 18)=\frac{1}{10}=0.10\).

Answer:

\(0.10\)