Question

Many people feel that the drying of pavement marking paint is much too slow. You spend several days looking for the fastest drying paint you can find; you plan to measure the time (in seconds) for this paint to dry. From information provided by the paint supplier, you believe the time to dry is normally distributed with a standard deviation of 3 seconds. How many paint samples would you need to test to be able to obtain an estimate of paint drying time that is within 2 seconds of the actual mean drying time with a probability of 99.5%?

Answer 1

Answer:

21

Step-by-step explanation:

Using Simple Random Sampling, we can estimate the sample size by the formula

$\bf n=\frac{Z^2S^2}{e^2}$

where  

n = sample size

Z = the z-score corresponding to the confidence level 99.5%

S = the assumed standard deviation = 3 seconds

e = margin of error = 2 seconds

It is worth noticing that the higher the confidence level, the larger the sample should be.

The z-score corresponding to a confidence level of 99.5% can be obtained either with a table or the computer and equals

Z = 3.023

Replacing the values in our formula

$\bf n=\frac{(3.023)^23^2}{2^2}=20.5616\approx 21$

So the size of the sample should be at least 21.