Question

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 5 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 31 minutes

(b) at most 20 minutes

Answer 1

Solution :

Given that ,

mean = = 25

standard deviation = = 5

(a)

P(x 31) = 1 - P(x   31)

= 1 - P((x - ) / (31 - 25) / 5)

= 1 -  P(z 1.2)  

= 1 - 0.8849   

= 0.1151

Probability = 0.1151

(b)

P(x 20)

= P[(x - ) / (20 - 25) / 5]

= P(z -1)

= 0.1587

Probability = 0.1587