Question

section 7.1 homework score: 2/16 answered: 2/16 question 3 the time it takes me to wash the dishes is uniformly distributed between 6 minutes and 14 minutes. what is the probability that washing dishes tonight will take me between 11 and 12 minutes? give your answer accurate to two decimal places.

Explanation:

Step1: Identify the formula for uniform - distribution probability

For a uniform distribution on the interval $[a,b]$, the probability density function is $f(x)=\frac{1}{b - a}$ for $a\leq x\leq b$, and the probability $P(c\leq X\leq d)=\frac{d - c}{b - a}$, where $a = 6$, $b = 14$, $c = 11$, and $d = 12$.

Step2: Calculate the probability

Substitute the values into the formula: $P(11\leq X\leq 12)=\frac{12 - 11}{14 - 6}=\frac{1}{8}=0.125$.
Rounding to two decimal places, we get $0.13$.

Answer:

$0.13$