Question

In: Statistics and Probability

. During a recent track meet, the average time for all people who ran the 100-meter...

. During a recent track meet, the average time for all people who ran the 100-meter dash was 11.4 seconds with a standard deviation of 0.6 seconds. Assuming the times were approximately normally distributed:

a. What percentage of runners finished in less than 10.5 seconds?

b. What percentage of runners finished in greater than 12 seconds?

c. If a runner wanted to be in the top (fastest) 20% of times, what time would she or he need to beat?

d. What percentage of runners finished between 10.5 and 12 seconds?

Expert Solution

P(z<Z) table :

a.

z = (10.5-11.4)/0.6 = -1.5

P(z<-1.5) = 0.0668 {from table}

P(x<10.5) = 0.0668

b.

z = (12-11.4)/0.6 = 1

P(z>1) = 1 - P(z<1)

= 1 - 0.8413

P(x>12) = 0.1587

c.

P(z<Z) = 1 - 0.20 = 0.80

Z = 0.84

time = mean+ 0.84*SD

= 11.4 + 0.84*0.6

= 11.904 seconds

d.

P(10.5<x<12) = 1 - P(x>12) - P(x<10.5)

= 1 - 0.1587 - 0.0668

= 0.7745

(please upvote)

orchestra answered 2 years ago

A recent study claims that people who travel for business spend an average of $78.00 per...

A recent study claims that people who travel for business spend an average of $78.00 per day on food. You suspect the real average is less than this. You conduct your own study and find that a random sample of 67 people who travel for business spend an average of $75.00 per day on food with standard deviation $12.00. Perform a hypothesis test using ∝ = 0.01 Step #1: State the null and alternative hypothesis. Identify the claim.Step #2: Find...

What is happening inside of the leg muscle cells of a runner during a 100-meter dash...

What is happening inside of the leg muscle cells of a runner during a 100-meter dash compared to a 2-mile race? What biochemical pathway(s) (aerobic respiration or anaerobic respiration) is/are being utilized in each race, and why? Explain why photosynthetic organisms are considered the ultimate source of food. What would happen to humans if all the plants died? ReplyForward

Design a simple database to track people and who they voted for. The database should have...

Design a simple database to track people and who they voted for. The database should have 3 tables: A table of candidates A table of registered voters A table of votes The candidate table should provide a listing of all candidates and information about the candidates. The registered voter table should hold all registered voters and any pertinent information about them The vote table should hold vote records for each candidate made by the voters Requirements: The system should not...

The swim buyer ran a sale during Memorial Day on all coverups at $29.99. The following...

The swim buyer ran a sale during Memorial Day on all coverups at $29.99. The following are the results that sold during the weekend event: 200 Sarong coverups with a regular retail price of $39.00 320 Cotton coverups with a regular retail price of $44.00 Calculate the Total $ markdown for the sale, the Total sales generated, and the Markdown % for the sale.

During a recent Ebola outbreak, researchers attempted extracting antibodies from people who had been infected but...

During a recent Ebola outbreak, researchers attempted extracting antibodies from people who had been infected but survived. They then injected other people with these antibodies to help them overcome the illness. Even more recently, an experimental vaccine against Ebola has been approved for emergency use in the Democratic Republic of the Congo. Ebola is a virus that infects macrophages and dendritic cells. In doing so, it causes dysregulation in several ways. For example, 1) it prevents infected cells from secreting...

A recent study shows that on average 21% of employees in the work population prefer their vacation time during March break.

A recent study shows that on average 21% of employees in the work population prefer their vacation time during March break. Vincent Company employs 55 people. Use the normal approximation to the binomial distribution to answer the questions below: Required: Determine the expected value, and the standard deviation of that value, of the number of Vincent Company employees who would prefer their vacation time during March break. What is the probability that more than nine Vincent Company employees will...

Economists often track employment trends by measuring the proportion of people who are “underemployed,” meaning they...

Economists often track employment trends by measuring the proportion of people who are “underemployed,” meaning they are either unemployed or would like to work full time but are only working part-time. In the summer of 2019, 18.5% of Americans were “underemployed.” The mayor of Detroit wants to show the voters that the situation is not as bad in his city as it is in the rest of the country. His staff takes a simple random sample of 400 Detroit residents...

The economic problem-how to meet the competing needs of all people with a fixed amount of...

The economic problem-how to meet the competing needs of all people with a fixed amount of money and resources-allows us an opportunity to discuss equity and equality. As a social worker, how would you recommend resolving the equity/equality discussion? If you had to grapple with solving the health care crisis, how would you do it equitably? Equally? Make sure you include a discussion of Social Work values and ethics and human rights issues.

How do we differentiate between people who are rude or mean versus those who meet diagnostic...

How do we differentiate between people who are rude or mean versus those who meet diagnostic criteria for antisocial personality disorder?

1. Economists often track employment trends by measuring the proportion of people who are “underemployed,” meaning...

1. Economists often track employment trends by measuring the proportion of people who are “underemployed,” meaning they are either unemployed or would like to work full time but are only working part-time. In the summer of 2019, 18.5% of Americans were “underemployed.” The mayor of Detroit wants to show the voters that the situation is not as bad in his city as it is in the rest of the country. His staff takes a simple random sample of 400 Detroit...