The state highway department is studying traffic patterns on one of the busiest highways in the state. As part of the study, the department needs to estimate the average number of vehicles that pass an intersection each day. A random sample of 64 days gives us a sample mean of 14,205 cars and a sample standard deviation of 1,010 cars. After calculating the confidence interval, the highway department officials decide that the precision is too low for their needs. They feel the precision should be 300 cars. Given this precision, and needing to be 99 percent confident, how many days do they need to sample

The need to sample 76 days.

Step-by-step explanation:

We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Ztable as such z has a pvalue of .

So it is z with a pvalue of , so

Now, find the margin of error M as such

In which is the standard deviation of the population and n is the size of the sample.

How many days do they need to sample

We need to sample n days.

n is found when M = 300.

We have that

So

Rounding up

The need to sample 76 days.

step-by-step explanation:

6 hours 48 min

step-by-step explanation:

68÷5=13.6

13.6×30=408min=6 hours 48 min.

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