Question

a new muscle relaxant is avalable. researchers from te firm developing the relaxant have done stuents that the time lapse between administrationof the drug and beginning effects of the drug is normally distributed, with population mean = 38 minutes and population standard deviation = 5minutes

a) the drug is administered to one patient selected at random. what is the probability that the time it takes to go into effects is 35 minutes of less?

b) the drug is administered to a random sample of 10 patients is 35 minutes or less?

c) comment on the differences in results in parts (a) and (b)

Answer 1

Solution:

Given that,

= 38

= 5

a ) p ( x  < 35 )

= p ( x -  / ) < ( 35 - 38 / 5)

= p ( z < - 3 / 5 )

= p ( z < - 0.6 )

Using z table

= 0.2743

Probability = 0.2743

b ) n = 10

So,

= 38

=  ( /n) = (5 / 10 ) = 1.5811

p (   < 35 )

= p ( -  / ) < ( 35 - 38 / 1.5811 )

= p ( z < - 3 / 1.5811 )

= p ( z < - 1.90 )

Using z table

= 0.0287

Probability = 0.0287

c )  The probability in part (b) is 0 0287 smaller than the same as larger than part (a) is 0.2743 because the standard deviation mean is ( a ) larger and (b ) smaller for the x distribution.