Answer to Question #25088 in Statistics and Probability for Carol Parducci

Question

It is said that sufferers of a cold virus experience symptoms for seven days. However, the amount of time is actually a normally distributed random variable whose mean is 7.5 days and whose standard deviation is 1.2 days. a. What proportion of cold sufferers experiences less than 4 days of symptoms? b. What proportion of cold sufferers experiences symptoms for between 7 and 10 days?

Answer 1

The normal distribution has probability density:
f(x) = 1/Sqrt[2 Pi]/sigma Exp[-(x -mean)^2/2/sigma^2)]
In our case
sigma = 1.2
mean = 7.5
a.& proportion of cold sufferers experiences less than 4 days of symptoms equals:
P(x<4) = Integrate[1/Sqrt[2 Pi]/1.2 Exp[-(x - 7.5)^2/2/1.2^2], {x, -Infinity, 4}] = 0.00176897 = 0.18 %
b.& proportion of cold sufferers experiences symptoms for between 7 and 10 days equals:
P(7<x<10) = Integrate[1/Sqrt[2 Pi]/1.2 Exp[-(x - 7.5)^2/2/1.2^2], {x, 7, 10}] = 0.642928 = 64.3 %