Ratio frequency identification (RFID) is an electronic scanning techno

Michael Dennis

Michael Dennis

Answered question

2021-11-17

Ratio frequency identification (RFID) is an electronic scanning technology that can be used to identify items in a number of ways. One advantage of RFID is that it can rliminate the need to manual count invertory, which can help improve invertory management. The technology is not infalible, however, and sometimes errors occurs when items are scanned. The probability that a scarring error occurs is 0.063. Complete parts a through d.
a) Find the probability that exactly 16 items will be scarred incorrectly from the next 4,600 items scanned.
b) Find the probability that more than 16 items will be scanned incorrectly from the next 4.600 items scanned
c) Find the probability that the number of items scanned incorrectly is between 14 and 16, irclusive, from the next 4,600 items scanned.

Answer & Explanation

Egreane61

Egreane61

Beginner2021-11-18Added 16 answers

Step 1
Poisson distribution is similar to binomial but it is used when there is large number of trials and the probability of success is very low. The probability distribution of poisson random variable is given by
P(x)=λxeλx!
The poisson parameter is λ=np where, n is total number of trials and p is the probability of success in each trial. Substitute n=4600 and p=28.98
λ=46000.0063
=28.98
Step 2
To find that exactly 16 items scanned incorrectly, substitute x=16 and λ=28.98 in the formula P(x)=λxeλx!
P(16)=28.9816e28.9816!
0.0031
Now, probability that the incorrect scan is more than 16 will be complement to probability that incorrect scan is smaller than 16. Using the calculator to find the P(x16) and then subtract the value from 1.
P(x>16)=1P(x16)
=10.00638
0.9936
Step 3
Now, it is asked to find P(14<x16) and to find this probability find the probability P(x16) and P(x14), then compute the difference between these two values.
Using the calculator, the values of P(x16=0.00638 and P(x14)=0.00161 To find the value of P(14<x16), subtract P(x14)=0.00161 from P(x16)=0.00638
P(14<x16)=0.006380.00161
0.0048

Do you have a similar question?

Recalculate according to your conditions!

New Questions in High school probability

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?