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.

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?

Answer: P (x ≤ 35) = 0.27

Step-by-step explanation:

Since the time lapse between administration of the drug and beginning effects of the drug is normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ) / σ

Where

x = the time lapse between administration of the drug and beginning effects of the drug

µ = mean time

σ = standard deviation

From the information given,

µ = 38 minutes

σ = 5 minutes

The probability that the time it takes to go into effect is 35 minutes or less is expressed as

P (x ≤ 35)

For x = 35,

z = (35 - 38) / 5 = - 0.6

Looking at the normal distribution table, the probability corresponding to the z score is 0.27