Finding percentiles using a normal distribution

Intro

Howdy!  I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help.  Today were going to learn how to find percentiles using a normal distribution.  Here's our problem statement: A common design requirement is that an environment must at the range of people fall between the 5th percentile for women in the 95th percentile for men.  For the design and assembly of a work table, the sitting knee height must be considered, which is the distance from the bottom of the feet to the top of the knee.  Males have sitting knee heights that are normally distributed with a mean of 21.7 inches and a standard deviation of 1.3 inches.  Females have sitting knee heights that are normally distributed with a mean of 19.6 inches and a standard deviation of 1.2 inches.  Use this information to answer the following questions.

Part 1

OK, the first question asks, “What is the minimum table clearance required to satisfy the requirement of sitting 95% of men?”  For this question, we really need our normal distribution calculator inside StatCrunch.  So I'm going to pull up StatCrunch, and I get my normal distribution calculator by going to Stat –> Calculators –> Normal.  Now I have a normal distribution calculator.

The question is asking about 95% of men, so I need the distribution for the men, and that's listed here in the problem statement.  So I'm going to adjust my mean and my standard deviation to match what’s there in the problem statement.  We want to fit 95% of men underneath the table, so the probability of 95% is in here in this field; it’s going to show me the answer that I'm looking for, which we compute comes out to 23.8 inches.  I put that here my answer field.  Nice work!

Part 2

OK, the second part of this problem says, “Determine if the following statement is true or false.  If there is clearance for 95% of males, there will certainly be clearance for all women in the bottom 5%.”  Well, that's probably true, because the bottom 5% for the women here the distribution the mean is 19.6, so that's definitely less then the 23.8 that we have here.  In the 5% for the women's been a be far less than the mean, so certainly going to be yes.

Although, if we wanted to prove it to ourselves, just put the distribution for the women here into our calculator inside StatCrunch and select to look for the bottom 5% that 17.6 which is less than 23.8.  So yes, the statement here is true.  So it has nothing to do with affect their outliers; it has to do with the 95th percentile for men being greater than the 5th percentile for women but tested.

Part 3

Now, the next part of the problem asks, “The author is writing this exercise at a the table with a clearance of 23.9 inches above the floor.  What percentage of men cam sit at this table?”  I need to put my distribution for men back here in my calculator.  The random variable here (23.9) and I'm going to get a percentage or probability coming out the other end.  So it looks like we want to round to two decimal places, so that's 95.47%.

Part 4

The next part of the problem asks us for the percentage of women that will fit under the table.  So we do the same thing, again putting in the summary statistics for my distribution for women and press Compute!  And it looks like — wow!  Just about all routes to distant places again.  Well done!

Part 5

And now the last part of the problem asks, “Does the table appear to be made to fit almost everyone?  Will the tables be fitting 95% of the men and practically all the women?”  So yeah, it will benefit almost everyone.  The only ones who will not fit will be about 5% of the men and a very, very small percentage of women.  Nice job!

And that's how we do it at Aspire Mountain Academy.  Be sure to leave your comments below and let us know how good a job we did or how we can improve.  And if your stats teacher is boring or just doesn't want to help you learn stats, go to aspiremountainacademy.com, where you can learn more about accessing our lecture videos or provide feedback on what you’d like to see.  Thanks for watching!  We’ll see you in the next video.