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# Threshold for low percentile

Find the cutoff for a given lower percentile in a normal distribution.

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• At , Sal mentioned that he wanted to find a z-score that represents a percentile that is barely less than 10%. What if the problem asked for top ten percent? Would we be looking for barely under or over 90%?
• for the top 10 percentile, you will look for barely over 90%,because suppose if you choose 89.98% then that is no longer in the top 10 %, however, if you choose 90.01% it is within top 10%.
• Why does Amelia vaule wait time over quality of food? That is the one question that remains after the video...
• How can you get the actual estimate of % on the density curve? I don't get how 10% was marked on that specific location (same goes with the previous lesson's 30%). Any guides that led to this?
• Good question Josh, Don't worry about this! As long as you know that you're looking for the 10% below (0.10) you should be able to find the z-score in the chart.
• Hi, I didn't understand one thing; since the distribution is normal (symetric) why you didn't take the second part (side) where the wait time is <10% I mean 185+1.29*11=199.19.
(1 vote)
• Maybe this is my programmer-brain, but I actually misread the question too at first, because I reasoned that the "bottom 10%" was going to be the restaurants with the longest waiting times. When I realized that it would be weird to go to restaurants that had the longest waiting times, I assumed that the bottom 10% meaned the bottom 10% of the distribution.

To be fair, the question doesn't specify!
• When you put the video speed on `0.25`, it sounds like everything Sal says is a question. XD
• Why is the z score -1.29?
(1 vote)
• What videos should i search for if i want to know the calculator version for this kind of
problem?
(1 vote)
• The type of calculator you have and then the function normalcdf
(1 vote)
• At . how did Sal know where the 10th percentile was, in relation to the SD?
(1 vote)
• You can calculate the probability from the cdf of a normal distribution. This is given in a table. From there you see the 10th percentile is between -2*(sigma) and -1*(sigma).
(1 vote)
• Ah!I found a problem! Isn't Z scores is from 0 to Z? so for this question 10% is actually 0.5-0.1=0.4 in z scores. We need to check the table for 0.4 rather than 0.1
(1 vote)