Answer:
Explanation:
We know that the time it takes to wash the dishes is uniformly distributed between 6 and 15 minutes. Let X be the time it takes to wash the dishes. Then, X ~ U(6, 15), where U represents the uniform distribution.
To find the probability that washing dishes tonight will take between 13 and 14 minutes, we need to find P(13 ≤ X ≤ 14). Since the distribution is uniform, the probability density function is f(x) = 1/(15-6) = 1/9 for 6 ≤ x ≤ 15.
The probability of a continuous random variable falling between two values is given by the integral of its probability density function between those values. So, we need to find:
P(13 ≤ X ≤ 14) = ∫13^14 f(x) dx
Substituting f(x) = 1/9, we have:
P(13 ≤ X ≤ 14) = (1/9) ∫13^14 dx
P(13 ≤ X ≤ 14) = (1/9) [x]13^14
P(13 ≤ X ≤ 14) = (1/9) [14 - 13]
P(13 ≤ X ≤ 14) = 1/9
Therefore, the probability that washing dishes tonight will take between 13 and 14 minutes is 1/9, or approximately 0.11 rounded to two decimal places.