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Ierofanga [76]
3 years ago
6

The time it takes me to wash the dishes is uniformly distributed between 10 minutes and 15 minutes. What is the probability that

washing dishes tonight will take me between 12 and 14 minutes
Mathematics
1 answer:
mario62 [17]3 years ago
5 0

Answer:

The probability that washing dishes tonight will take me between 12 and 14 minutes is 0.1333.

Step-by-step explanation:

Let the random variable <em>X</em> represent the time it takes to wash the dishes.

The random variable <em>X</em> is uniformly distributed with parameters <em>a</em> = 10 minutes and <em>b</em> = 15 minutes.

The probability density function of <em>X</em> is as follows:

f_{X}(x)=\frac{1}{b-a};\ a

Compute the probability that washing dishes will take between 12 and 14 minutes as follows:

P(12\leq X\leq 14)=\int\limits^{12}_{14} {\frac{1}{15-10} \, dx

                           =\frac{1}{5}\int\limits^{12}_{14} {1} \, dx \\\\=\frac{1}{5}\times [x]^{14}_{12}\\\\=\frac{1}{15}\times [14-12]\\\\=\frac{2}{15}\\\\=0.1333

Thus, the probability that washing dishes tonight will take me between 12 and 14 minutes is 0.1333.

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