__Exercise 1__

Births are approximately uniformly distributed between the 52 weeks of the year. They can be said to follow a Uniform Distribution from 1 – 53 (spread of 52 weeks).

1. Graph this density curve.

2. Find the proportion of babies born after the 40th week of the year

3. Find the proportion of babies born before the 10th week of the year

4. Find the proportion of babies born between the 10th and 40th week of the year

5. What is the 70th percentile?

I have had some experience with these types of problems, but the part's throwing me off is that the distribution follows from 1-53... so does this mean that when I graph it, the graph will be a solid line, going from x=1 to x=53? And additionally, would the height then be 1/52 to make it so that the area under the curve = 1? My approach to the second part was to do 53-40=13(1/52)=13/52=1/4... is that correct? Additionally, to find the 70th percentile, do I do 0.7(53)? or 0.7(520? or 0.7(52) and add it to 1, since that is where the graph starts?

__Exercise 2__

A random number generator picks a number from 1 to 9 in a uniform manner

1. Graph this density curve.

2. Find the proportion of times a number between 3.5 and 7.25 is chosen.

3. Find the proportion of times a number over 5.67 is chosen.

4. Find the 90th percentile.

5. Find the median of the numbers chosen.

Again, the issue I encountered with this problem was that it said 1-9... so would my graph go from x=1 to x=9? and would the height be 1/8 or 1/9, considering 9-1=8, but at the same time the question says numbers 1-9? How would I approach finding the 90th percentile... and how would I find the median? Would it be 5, as it is between 1-9?

rithu Jul 29, 2023