Question

researchers at a drug company are testing the duration of a new pain reliever. the drug is normally distributed with a mean durtion of 240 minutes and a standard deviation of 40 minutes the drug is administered to a random sample of 10 people..what is the populatin mean? what is the standard deviation? what is the sample size? can normal approximation be use for this problem? what is the mean of the samle means? what is the standard deviation of the sample means? what is the probability that the drug will wear off in less than 200 minutes? what is the z score? what is the requested probability? wht is the probability the drug will wear off in 220 minutes? what is the probability that the drug will wear off between 200 and 220 minutes

Answer 1

Solution :

Given that ,

mean = = 240

standard deviation = = 40

n = 10

= 240  

= / n = 40 / 10  = 12.6491

P( < 200)

= P(( - ) / < ( 200 - 240) / 12.6491 )

= P(z < -3.16 )

The z score = -3.16

Using z table

= 0.0008

Probability = 0.0008

P( < 220 )

= P(( - ) / < ( 220 - 240) / 12.6491 )

= P(z < -1.58 )

Using z table

= 0.0571

Probability = 0.0571

P( 200 < < 220 )  

= P[( 200 - 240) / 12.6491 < ( - ) / < ( 220 - 240) / 12.6491)]

= P( -3.16 < Z < -1.58 )

= P(Z < -1.58) - P(Z < -3.16 )

Using z table,  

= 0.0571 - 0.0008

= 0.0563

Probability = 0.0563