Diagnosing stroke strictly on the basis of clinical symptoms isdifficult. A stan
ID: 2914648 • Letter: D
Question
Diagnosing stroke strictly on the basis of clinical symptoms isdifficult. A standard diagnostic test used in clinicalmedicine to detect stroke in patients is the angiogram. Thistest has some risks for the patient, and researchers have developedseveral noninvasive techniques that they hope will be as effectiveas the angiogram. One such method uses measurement ofcerebral blood flow (CBF) in the brain, because stroke patientstend to have lower CBF levels than normal. Assume that in thegeneral population, CBF is normally distributed with mean 75 andstandard deviation 17. A patient is classified as being atrisk for stroke if his or her CBF is lower than 40.Part 1. What proportion of normal patients will beclassified as being at risk for stroke?
Part 2. What is the probability that a randomsample of 25 normal patients will have a mean CBF greater than40?
Part 1. What proportion of normal patients will beclassified as being at risk for stroke?
Part 2. What is the probability that a randomsample of 25 normal patients will have a mean CBF greater than40?
Explanation / Answer
mean , = 75standard deviation, = 17 Part 1. What proportion of normal patients will be classifiedas being at risk for stroke? A patient is classified as being at risk for stroke if his or herCBF is lower than 40. P(X<40) = P(Z<(X-)/) =P(Z<(40-75)/17)=P(Z<-2.06) =0.0197 hence, proportion of normal patients will be classified as being atrisk for stroke =0.0197
Part 2. What is the probability that a random sample of25 normal patients will have a mean CBF greater than 40? n=25 standard error, e = /n = 17/5 = 3.4 P(X>40) = P(Z>(X-)/e) =P(Z>(40-75)/3.4)=P(Z>-10.3) ˜1-0 = 1 probability that a random sample of 25 normal patients willhave a mean CBF greater than 40 =1 mean , = 75
standard deviation, = 17 Part 1. What proportion of normal patients will be classifiedas being at risk for stroke? A patient is classified as being at risk for stroke if his or herCBF is lower than 40. P(X<40) = P(Z<(X-)/) =P(Z<(40-75)/17)=P(Z<-2.06) =0.0197 hence, proportion of normal patients will be classified as being atrisk for stroke =0.0197
Part 2. What is the probability that a random sample of25 normal patients will have a mean CBF greater than 40? n=25 standard error, e = /n = 17/5 = 3.4 P(X>40) = P(Z>(X-)/e) =P(Z>(40-75)/3.4)=P(Z>-10.3) ˜1-0 = 1 probability that a random sample of 25 normal patients willhave a mean CBF greater than 40 =1 Part 1. What proportion of normal patients will be classifiedas being at risk for stroke? A patient is classified as being at risk for stroke if his or herCBF is lower than 40. P(X<40) = P(Z<(X-)/) =P(Z<(40-75)/17)=P(Z<-2.06) =0.0197 hence, proportion of normal patients will be classified as being atrisk for stroke =0.0197
Part 2. What is the probability that a random sample of25 normal patients will have a mean CBF greater than 40? n=25 standard error, e = /n = 17/5 = 3.4 P(X>40) = P(Z>(X-)/e) =P(Z>(40-75)/3.4)=P(Z>-10.3) ˜1-0 = 1 probability that a random sample of 25 normal patients willhave a mean CBF greater than 40 =1 P(X>40) = P(Z>(X-)/e) =P(Z>(40-75)/3.4)=P(Z>-10.3) ˜1-0 = 1 probability that a random sample of 25 normal patients willhave a mean CBF greater than 40 =1