1) The manager of a warehouse would like to know how many errors are made when a product’s serial number is read by a bar-code reader. There are 24 errors after 1000 scans. Is it reasonable for the manager to expect less than 5% errors in 1000 scans?
2) Just to be sure, the manager has more samples taken. There are 36 errors after 1000 scans. Is t reasonable for the manager to expect less than 5% errors in 1000 scans?
Yes and yes.
To determine whether it is reasonable for the manager to expect less than 5% errors in 1000 scans, we need to calculate the proportion of errors in the samples provided.
1) For the first sample of 1000 scans, there were 24 errors. The proportion of errors can be calculated by dividing the number of errors by the total number of scans: 24/1000 = 0.024.
2) For the second sample of 1000 scans, there were 36 errors. The proportion of errors can be calculated by dividing the number of errors by the total number of scans: 36/1000 = 0.036.
Now, let's compare these proportions to 5%, which is equivalent to 0.05.
1) For the first sample, the proportion of errors is 0.024. Since 0.024 is less than 0.05, it is reasonable for the manager to expect less than 5% errors in 1000 scans based on this sample.
2) For the second sample, the proportion of errors is 0.036. Since 0.036 is also less than 0.05, it is reasonable for the manager to expect less than 5% errors in 1000 scans based on this sample as well.
In conclusion, based on the provided samples, it is reasonable for the manager to expect less than 5% errors in 1000 scans.
To determine whether it is reasonable for the manager to expect less than 5% errors in 1000 scans, we can calculate the error rate and compare it to the threshold of 5%.
1) For the first scenario, with 24 errors after 1000 scans, we can calculate the error rate as follows:
Error Rate = (Number of Errors / Number of Scans) * 100
= (24 / 1000) * 100
= 2.4%
Since the error rate of 2.4% is less than the threshold of 5%, it is reasonable for the manager to expect less than 5% errors in 1000 scans.
2) For the second scenario, with 36 errors after 1000 scans, we can calculate the error rate as follows:
Error Rate = (Number of Errors / Number of Scans) * 100
= (36 / 1000) * 100
= 3.6%
Similar to the first scenario, the error rate of 3.6% is less than the threshold of 5%, indicating that it is still reasonable for the manager to expect less than 5% errors in 1000 scans.
In both cases, the error rate is below the threshold of 5%, so it is reasonable for the manager to expect less than 5% errors in 1000 scans.