Question

The time taken to assemble a car in a certain plant is a random variable having a mean of 20 hours. if 6.3% of the cars assembled take longer than 25 hours. find the standard deviation of assembly time?

Answer 1

The standard deviation of assembly time is 2.58 hours.

Step-by-step explanation:

We are given that the time taken to assemble a car in a certain plant is a random variable having a mean of 20 hours.

Also, 6.3% of the cars assembled take longer than 25 hours.

Let X = time taken to assemble a car in a certain plant

The z score probability distribution for normal distribution is given by;

                                Z  =  $\frac{X-\mu}{\sigma}$  ~ N(0,1)

where, $\mu$ = population mean assembly time = 20 hours

            $\sigma$ = standard deviation

Now, it is given that 6.3% of the cars assembled take longer than 25 hours, that means;

                   P(X > 25 hours) = 6.3%

                   P( $\frac{X-\mu}{\sigma}$ > $\frac{25-20}{\sigma}$ ) = 0.063

                   P(Z > $\frac{4}{\sigma}$ ) = 0.063

Now, in the z table the critical value of x which represents a top area of 6.3% is given as 1.5504, that means;

                            $\frac{4}{\sigma} = 1.5504$

                            $\sigma=\frac{4}{1.5504}$ = 2.58 hours

Therefore, the standard deviation of assembly time is 2.58 hours.