Question

The times between parts arrive a manufacturing station is exponentially distributed with mean of 0.5 minute.

What is the value of parameter?

What is the median time between the parts arrive?

What is the standard deviation?

What is the 80^th percentile?

Find the probability of that more than 1 minute elapse between part arrivals.

After manufacturing, computer disks are tested for errors. Let X be the number of errors detected on a randomly chosen disk. The following table presents the probability mass function of X.

X   P(X)

0   0.48

1   0.39

2   0.12

3   0.01

What is the mean and standard variation of the error in this manufacturing process?

A sample of 225 disks is drawn from the process. Find out the probability of fewer than 110 of these disks have no errors

Answer 1

Ans:

1)Given that

mean=0.5 minute

a) $\lambda =1/0.5=2$

b)P(T<=t)=0.5

1-e^-2t=0.5

$2t=-ln(0.5)=0.6931$

$t=0.6931/2=0.3466$ min

c)standard deviation=1/2=0.5

d)80th percentile means that

P(T<=t)=0.8

1-e^-2t=0.8

e^-2t=0.2

2t=-ln 0.2=1.609

t=0.8047 min

e)P(T>1)=1-P(T<=1)=e^-2=0.1353