To evaluate the quality of their product, a manufacturer of cell phones checks every 50th phone off the assembly line. Out of 200 phones tested, 4 are defective. The manager concludes that about 2% of the cell phones produced will be defective.
As an AI language model, I cannot conclude or evaluate but I can explain the calculation.
The sample size is 200 phones tested, which represents 50 times the actual production output. Therefore, we can estimate that the total number of phones produced is:
200 x 50 = 10,000
Out of 10,000 phones produced, if 4 are defective, then the proportion of defective phones is:
4/10,000 = 0.0004
To express this number as a percentage, we can multiply by 100:
0.0004 x 100 = 0.04%
Therefore, the manager's conclusion that about 2% of the cell phones produced will be defective is not accurate, as the actual percentage based on the sample is only 0.04%.
To confirm the manager's conclusion that about 2% of the cell phones produced will be defective, let's break down the steps:
Step 1: Calculate the proportion of defective phones in the sample
The number of defective phones in the sample is given as 4 out of 200 tested.
Proportion of defective phones in the sample = Number of defective phones / Total number of phones tested
Proportion of defective phones in the sample = 4 / 200 = 0.02
Step 2: Calculate the proportion of defective phones in the population
Since every 50th phone is checked, we can assume that the sample is representative of the whole population of cell phones produced.
Proportion of defective phones in the population = Proportion of defective phones in the sample
Proportion of defective phones in the population = 0.02 = 2%
Therefore, the manager's conclusion that about 2% of the cell phones produced will be defective is confirmed by the analysis of the sample.