Question

In a certain store, there is a 0.02 probability that the scanned price in the bar code scanner will not match the advertised price. The cashier scans 835 items.

(a-1)

What is the expected number of mismatches? (Round your answer to the nearest whole number.)

Expected number

(a-2)

What is the standard deviation? (Use your rounded number for the expected number of mismatches for the calculation of standard deviation. Round your final answer to 4 decimal places.)

Standard deviation

(b)	What is the probability of at least 9 mismatches? (Round the z-value to 2 decimal places. Use Appendix C-2 to find probabilities. Round your final answer to 4 decimal places.)

Probability

(c)	What is the probability of more than 27 mismatches? (Round the z-value to 2 decimal places. Use Appendix C-2 to find probabilities. Round your final answer to 4 decimal places.)

Probability

References

eBook & Resources

Answer 1

Let us assume that 835 items are independent. Further here p=0.02 is same for all, n=835 is constant and events are independent

a-1. Mean=np=0.02*835=16.7

a-2. Standard deviation is

b. As n is sufficient large and np>10 and n(1-p)>10, we can assume normal distribution

So

As distribution is approximate normal we can convert this to z

d.