In: Statistics and Probability
The amount of time between taking a pain reliever and getting relief is normally distributed with a mean of 25 minutes and a standard deviation of 3 minutes. Find the probability that the time between taking the medication and getting relief is as follows. (Round your answers to four decimal places.)
(a) at least 33 minutes
(b) at most 20 minutes
Solution :
Given that,
mean = = 25
standard deviation = = 3
P(x >33 ) = 1 - P(x<33 )
= 1 - P[(x -) / < (33-25) /3 ]
= 1 - P(z < 2.67)
Using z table
= 1 - 0.9962
probability =0.0038
b.
P(x20 )
= P[(x -) / (20-25) /3 ]
= P(z -1.67)
Using z table
= 0.0475
probability =0.0475