Problem 85

Given that a NUMMI assembly line, which has been operating since 1984, has built an average of 6,000 cars and trucks a week. Generally, 10% of the cars were defective coming off the assembly line. Suppose we draw a random sample of n = 100 cars. Let X represent the number of defective cars in the sample. Then we have to analyze and say about X in regard to the 68-95-99.7 empirical rule (one standard deviation, two standard deviations, and three standard deviations from the mean are being referred to). Assume a normal distribution for the defective cars in the sample.

Step 1.

According to the given information,  represent the number of defective cars in the sample.

 

Then ~   

 

where  n=100, p=0.1 then q=1-p=1-0.1=0.9

 

 

 

As n is large, np and nq>5 Normal approximation used. 

 

So mean  

 

and standard deviation  

 

So ~