Question

A new muscle relaxant is available. Researchers from the firm developing the relaxant have done studies that indicate that the time lapse between administration of the drug and beginning effects of the drug is normally distributed, with mean μ = 38 minutes and standard deviation σ = 5 minutes.

(a) The drug is administered to one patient selected at random. What is the probability that the time it takes to go into effect is 35 minutes or less? (Round your answer to four decimal places.)


(b) The drug is administered to a random sample of 10 patients. What is the probability that the average time before it is effective for all 10 patients is 35 minutes or less? (Round your answer to four decimal places.)


(c) Comment on the differences of the results in parts (a) and (b).

The probability in part (b) is  ---Select--- smaller than larger than the same as part (a) because the  ---Select--- mean standard deviation is  ---Select--- larger smaller for the x distribution.

Answer 1

a)

for normal distribution z score =(X-μ)/σx
here mean=       μ=	38
std deviation   =σ=	5.0000

probability =

P(X<35)

=

P(Z<-0.6)=

0.2743

b)

sample size       =n=	10
std error=σx̅=σ/√n=	1.5811

probability =

P(X<35)

=

P(Z<-1.9)=

0.0287

c)

The probability in part (b) is smaller than as part (a) because the standard deviation is  smaller for the x distribution.