SOLUTION: None of my formulas are working on this,please help! A new muscle relaxant is available. Researchers from the firm developing the relaxant have done studies that indicate that the

Question 1076031: None of my formulas are working on this,please help!
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).

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
mean is 38, sd is 5
z=(x-mean)/sd
z<(35-38)/5, so looking for probability that z < -0.6
probability (z<-0.6)=0.2743
================================
For the MEAN of 10 people, z=(x-mean)/sigma/sqrt(n)
=-.6/5/sqrt(10)=-6 sqrt (10)/5 or z < -3.79=0.00007
It is not unlikely to have one person get the effect under 35 minutes, but for a mean of 10 people, it is far less likely.

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