Respuesta :
Answer:
The probability of assembling the product between 7 to 9 minutes is 0.50.
Step-by-step explanation:
Let X = assembling time for a product.
Since the random variable is defined for time interval the variable X is continuously distributed.
It is provided that the random variable X is Uniformly distributed with parameters a = 6 minutes and b = 10 minutes.
The probability density function of a continuous Uniform distribution is:
[tex]f_{X}(x)=\left \{ {{\frac{1}{b-a};\ a<X<b,\ a<b} \atop {0;\ otherwise}} \right.[/tex]
Compute the probability of assembling the product between 7 to 9 minutes as follows:
[tex]P(7<X<9)=\int\limits^{9}_{7}{\frac{1}{10-6}}\, dx\\[/tex]
[tex]=\frac{1}{4}\times \int\limits^{9}_{7}{1}\, dx[/tex]
[tex]=\frac{1}{4}\times [x]^{9}_{7}\\[/tex]
[tex]=\frac{1}{4}\times (9-7)\\[/tex]
[tex]=\frac{1}{2}\\=0.50[/tex]
Thus, the probability of assembling the product between 7 to 9 minutes is 0.50.
The probability of assembling the product between 7 to 9 minutes is 0.50.
What is probability?
Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.
The assembly time for a product is uniformly distributed between 6 to 10 minutes.
Let X be the assembling time for the product.
It is provided that the random variable X is uniformly distributed is
[tex]\rm f_x(x) = \left\{\begin{matrix} \frac{1}{b-a}; a < X < b, a < b \\\\0; otherwise\end{matrix}\right.[/tex]
Compute the probability of assembling the product between 7 to 9 minutes.
[tex]\rm P(7 < X < 9) = \int ^9_7 \dfrac{1}{10-6} dx\\\\P(7 < X < 9) = \dfrac{1}{4} [x]^9_7\\\\P(7 < X < 9) = \dfrac{1}{4} (9-7)\\\\P(7 < X < 9) = \dfrac{1}{4} * 2\\\\P(7 < X < 9) = 0.50[/tex]
Thus, the probability of assembling the product between 7 to 9 minutes is 0.50.
More about the probability link is given below.
https://brainly.com/question/795909
