F we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, find the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 3 minutes. You should use the finite population correction factor for this problem. True False

And we can find this probability with the normal standard table or excel and we got:

And for this case is not neccesary applt the finite population correction factor since the distribution for the random variable is assumed known and normal

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the length of time of a population, and for this case we know the distribution for X is given by:

Where and

We are interested on this probability

And the best way to solve this problem is using the normal standard distribution and the z score given by:

If we apply this formula to our probability we got this:

And we can find this probability with the normal standard table or excel and we got:

And for this case is not neccesary applt the finite population correction factor since the distribution for the random variable is assumed known and normal

the answer is 5636.7