Res/341 Questions
21. In a recent study 90 percent of the homes in the United States were found to have color TVs. In a sample of nine homes, what is the probability that:
a. All nine have color TVs?
.387
b. Less than five have color TVs?
.008
c. More than five have color TVs?
.998
d. At least seven homes have color TVs?
6.955
46. Thirty percent of the population in a southwestern community are Spanish-speaking Americans. A Spanish-speaking person is accused of killing a non-Spanish-speaking American. Of the first 12 potential jurors, only 2 are Spanish-speaking Americans, and 10 are not. The defendant’s lawyer challenges the jury selection, claiming bias against her client. The government lawyer disagrees, saying that the probability of this particular jury composition is common. What do you think?
If the jury pool remained 2 are Spanish speaking Americans, it is only 17% of the pool that is Spanish speaking – which is not even close to the 30% population of Spanish speaking Americans in the southwest.
To make it more fair, the percentage of Spanish speaking jurors should be at or close to 30%. Which makes it between 3-4 jurors who speak Spanish.
105. The Director of Emergency Medicine at Big Mountain Medical Services is studying patient waiting time. Waiting time is defined as the time from when a patient enters the facility until seen by a physician. The study indicates the waiting time follows a normal distribution with a mean of 22 minutes and a standard deviation of 8 minutes.
a. What fraction of the patients is seen in between 15 and 22 minutes?
31.06%
b. What fraction is seen in less than 15 minutes?
P (minutes < 15) = .1922 Answer: 19.22%
c. What fraction is seen in more than 15 minutes but less than 32 minutes?
P (15 < minutes < 32) = .7003 Answer: 70.03%
d. What fraction is seen in more than 25 minutes but less than 32 minutes?
P (25 < minutes < 32) = .0222 Answer: 2.22%
e. Five percent of the patients are seen in how many minutes or less?
a. All nine have color TVs?
.387
b. Less than five have color TVs?
.008
c. More than five have color TVs?
.998
d. At least seven homes have color TVs?
6.955
46. Thirty percent of the population in a southwestern community are Spanish-speaking Americans. A Spanish-speaking person is accused of killing a non-Spanish-speaking American. Of the first 12 potential jurors, only 2 are Spanish-speaking Americans, and 10 are not. The defendant’s lawyer challenges the jury selection, claiming bias against her client. The government lawyer disagrees, saying that the probability of this particular jury composition is common. What do you think?
If the jury pool remained 2 are Spanish speaking Americans, it is only 17% of the pool that is Spanish speaking – which is not even close to the 30% population of Spanish speaking Americans in the southwest.
To make it more fair, the percentage of Spanish speaking jurors should be at or close to 30%. Which makes it between 3-4 jurors who speak Spanish.
105. The Director of Emergency Medicine at Big Mountain Medical Services is studying patient waiting time. Waiting time is defined as the time from when a patient enters the facility until seen by a physician. The study indicates the waiting time follows a normal distribution with a mean of 22 minutes and a standard deviation of 8 minutes.
a. What fraction of the patients is seen in between 15 and 22 minutes?
31.06%
b. What fraction is seen in less than 15 minutes?
P (minutes < 15) = .1922 Answer: 19.22%
c. What fraction is seen in more than 15 minutes but less than 32 minutes?
P (15 < minutes < 32) = .7003 Answer: 70.03%
d. What fraction is seen in more than 25 minutes but less than 32 minutes?
P (25 < minutes < 32) = .0222 Answer: 2.22%
e. Five percent of the patients are seen in how many minutes or less?