In a simple random sample of 70 automobiles registered in a certain state, 25 of them were found to have emission levels that exceed a state standard. Find a 95% lower confidence bound for the proportion of automobiles whose emissions exceed the standard. Round the answer to three decimal places.

The 95% lower confidence bound is  a = 0.2451

Step-by-step explanation:

From the question we are told that

    The sample size is  n  =  70

   The number that have emission level that exceed a state standard is  k =  25

   Generally the sample proportion is mathematically represented as

=>      

=>      

From the question we are told the confidence level is  95% , hence the level of significance is    

=>  

Generally from the normal distribution table the critical value  of   is  

Generally the margin of error is mathematically represented as  

=>  

=>  

Generally 95% confidence interval is mathematically represented as  

=>    

=>    

The 95% lower confidence bound is  a = 0.2451

she will travel a distance in the range of 3 - 11 miles