Forty percent of business travelers carry either a cell phone or a laptop. For a sample...

Forty percent of business travelers carry either a cell phone or a laptop. For a sample of 15 business travelers, make the following calculations.

a. Compute the probability that three of the travelers carry a cell phone or laptop.

b. Compute the probability that 12 of the travelers carry neither a cell nor a laptop.

c. Compute the probability that at least three of the travelers carry a phone or a laptop.

Expert Solution

First of all check whether all assumptions of binomial distribution is satisfied or not -

The four characteristic of binomial distribution is -

1)The number of observations n=15 is fixed.
2)Each observation is independent.
3)Each observation represents one of two outcomes ("Carry " or " not carry").
4)The probability of "success" p=0.4 is the same for each outcome.

To get the probability the respective probabilities
consider, X- Number of business travelers carry either a cell phone or a laptop
Then X~Bin(15,0.4)
a) probability that three of the travelers carry a cell phone or laptop= P(X=3) =0.0634
( This is obtained using the excel command "=Binomdist(number,trail,probability,cumulative)",here number=3,trail =15 ,probability =0.4 ,cumulative = False in above command)

b) probability that 12 of the travelers carry neither a cell nor a laptop= 1- P(X=12) =1-0.0016=0.9984
( This is obtained using the excel command "=Binomdist(number,trail,probability,cumulative)",here number=12,trail =15 ,probability =0.4 ,cumulative = False in above command)

c) probability that at least three of the travelers carry a phone or a laptop= P(X<=3) =0.0905

( This is obtained using the excel command "=Binomdist(number,trail,probability,cumulative)",here number=3,trail =15 ,probability =0.4 ,cumulative = True in above command)

orchestra answered 2 years ago

Forty five percent of employees in a firm are female. A sample of 49 employees is...

Forty five percent of employees in a firm are female. A sample of 49 employees is selected randomly. What is the probability that the sample proportion of females is at least 0.45?

A random sample found that forty percent of 50 Americans were satisfied with the gun control...

A random sample found that forty percent of 50 Americans were satisfied with the gun control laws in 2017. Compute a 97% confidence interval for the true proportion of Americans who were satisfied with the gun control laws in 2017. Fill in the blanks appropriately. A 97% for the true proportion of Americans who were satisfied with the gun control laws in 2017 is: Answer= (___ ,___ ) (Keep 3 decimal places)

A random sample found that forty percent of 100 Americans were satisfied with the gun control...

A random sample found that forty percent of 100 Americans were satisfied with the gun control laws in 2017. Compute a 99% confidence interval for the true proportion of Americans who were satisfied with the gun control laws in 2017. Fill in the blanks appropriately. A random sample found that forty percent of 100 Americans were satisfied with the gun control laws in 2017. Compute a 99% confidence interval for the true proportion of Americans who were satisfied with the...

In 2003, forty percent of the students at a major university were Business majors, 35% were...

In 2003, forty percent of the students at a major university were Business majors, 35% were Engineering majors and the rest of the students were majoring in other fields. In a sample of 600 students from the same university taken in 2004, two hundred were Business majors, 220 were Engineering majors and the remaining students in the sample were majoring in other fields. At 95% confidence, test to see whether there has been a significant change in the proportions between...

in the article "the relationship between cell phone use and academic performance in a sample of...

in the article "the relationship between cell phone use and academic performance in a sample of U.S. college students" anwers this question what were the major limits ( generalizability, something not measured in the current study that may be have affected the results) of the study according to the author ? you?

One recent survey of cell phone usage around the world showed that only 4 percent of...

One recent survey of cell phone usage around the world showed that only 4 percent of people in countries like Uganda and Ethiopia have access to a smartphone. Explain how this presents an opportunity for these countries to attain faster growth. What are the likely costs of economic growth? Suppose that you are currently getting your undergraduate degree and are considering going on for a graduate degree. You expect that once you have your graduate degree, your income and your...

Seventy three percent of drivers carry jumper cables in their vehicles. from a random sample of...

Seventy three percent of drivers carry jumper cables in their vehicles. from a random sample of 315 driver A. What is the probability that exactly 225 carry jumper cables in their vehicle B. What is the probability that at most 225 carry jumper cables in their vehicle C. What is the probability that more than 210 carry jumper cables in their vehicle D. What is the mean value of the number of driver that carry jumper cable in their vehicle...

A 2009 Pew Research Survey of a nationally representative sample of 242 cell phone users, aged...

A 2009 Pew Research Survey of a nationally representative sample of 242 cell phone users, aged 16 to 17 years, found that 52% had talked on the phone while driving. 1. Find a 98% confidence interval for the percentage of all cell phone users aged 16 to 17 years old who have talked on the phone while driving. 2. Do these data provide evidence that a majority of 16 to 17 year old cell phone users talk on the phone...

A major insurance company looked at teen cell phone use, specifically while driving. Eighty-two percent were...

A major insurance company looked at teen cell phone use, specifically while driving. Eighty-two percent were using phones in the sample of fifty drivers. a. Construct the 95% confidence interval for the proportion of all teenagers that have used cell phones while driving. (Round answers to 2 decimal places.) b. What is the margin of error with 95% confidence? (Round answer to 2 decimal places.)

Seventy-six percent of small business owners do not have a college degree. If a random sample...

Seventy-six percent of small business owners do not have a college degree. If a random sample of 60 small business owners are selected, find the probability that exactly 50 will not have a college degree.

Question