Question

Radio 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 eliminate the need to manually count​ inventory, which can help improve inventory management. The technology is not​ infallible, however, and sometimes errors occur when items are scanned. The probability that a scanning error occurs is 0.0069. Use​ Excel's binom.dist function to complete parts a through c. a. Find the probability that exactly 30 items will be scanned incorrectly from the next 5 comma 300 items scanned. The probability is nothing. ​(Round to four decimal​ places.) b. Find the probability that more than 30 items will be scanned incorrectly from the next 5 comma 300 items scanned. The probability is nothing. ​(Round to four decimal​ places.) c. Find the probability that the number of items scanned incorrectly is between 16 and 30​, ​inclusive, from the next 5 comma 300 items scanned. ​Hint: Find the probability of less than or equals 30 items being scanned incorrectly. Then subtract from it the probability of less than or equals 16 items being scanned incorrectly. The probability is nothing. ​(Round to four decimal​ places.)

Answer 1

Answer:

a) 0.0387; b) 0.8435; c) 0.1564

Step-by-step explanation:

Using a graphing calculator, for part a, we use Bpd, binomial probability distribution.

In this problem, n = 5300 since it is the number of trials.  The probability of success, or in this case the probability that the items are scanned incorrectly, is 0.0069.  For part a, x = 30; running this on the calculator, we get 0.0387.

For part b, we will use Bcd, the cumulative binomial distribution.  Our number of trials is still 5300, and our p (probability of success) is still 0.0069.  In this question, x is still 30.  The Bcd function will give us the probability that less than or equal to 30 are scanned incorrectly; this means once we find this value, we subtract from 1.

The calculator gives us 0.1565; this means our answer for part b is 1-0.1565 = 0.8435.

For part c, we already have the probability of less than 30 items being scanned from part b; this is 0.1565.

The probability of less than or equal to 16 items being scanned incorrectly is 0.000106.  To find the probability between these values we subtract:

0.1565-0.000106 = 0.156394 ≈ 0.1564