Question

The assembly time for a product is uniformly distributed between 6 to 10 minutes. The probability of assembling the product between 7 to 9 minutes is

Answer 1

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:

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

Compute the probability of assembling the product between 7 to 9 minutes as follows:

$P(7$

                      $=\frac{1}{4}\times \int\limits^{9}_{7}{1}\, dx$

                      $=\frac{1}{4}\times [x]^{9}_{7}$

                      $=\frac{1}{4}\times (9-7)$

                      $=\frac{1}{2}\\=0.50$

Thus, the probability of assembling the product between 7 to 9 minutes is 0.50.