The probability that it will snow on any given day in January in Chicago is \(26\%\). Use this applet (located at the bottom of the page) to investigate the probability of it snowing on any given number of days.
From the drop down menu that says normal click on binomial. Enter \(31\) for \(n\) and \(.26\) for \(p\) as seen here in the picture.
From the drop down menu that says normal click on binomial. Enter \(31\) for \(n\) and \(.26\) for \(p\) as seen here in the picture.
To answer the questions below, you can find the answers by editing the values for \(P\) in the input boxes as seen here.
If you put the same number in the boxes, as in the picture, it will calculate the probability that it will snow exactly \(4\) days in January. Otherwise, you can put a range of numbers, finding the probability that it will snow between \(3\) and \(8\) days, for example.
a) What is the probability that it will snow \(8\) days?
b) What is the probability that it will snow \(12\) days?
c) What is the probability that it will snow between \(1\) and \(7\) days?
d) What is the probability that it will snow more than \(10\) days?
e) What is the probability that it will snow no more than \(10\) days?
f) What is the probability that it will snow at least one day?
g) Describe the shape of the probabilities. Why do you think the graph is in this shape?