Assume that 40% of graduates come from University A and and earn salaries of 30,000 on...

Assume that 40% of graduates come from University A and and earn salaries of 30,000 on average with a standard deviation of 5,000. The remainder come from University B and earn salaries of 25,000 on average with a standard deviation of 7,500. If you are told that a graduate is earning less than 35,000, what is the probability that they came from University A? (Assume salaries are normally distributed.)

Solutions

Expert Solution

P(z<Z) table :

P(universitiy A) = 0.40

P(universitiy B) = 0.60

P(salary <= 35000 | universitiy A) :

P(salary <= 35000 | universitiy A) = 0.8413

P(salary <= 35000 | universitiy B) :

P(salary <= 35000 | universitiy B) = 0.9088

P(salary <= 35000) = P(salary <= 35000 | universitiy A)*P(universitiy A) + P(salary <= 35000 | universitiy B)*P(universitiy B)

= 0.8413*0.40 + 0.9088*0.60

= 0.8818

P(university A | salary <= 35000) = P(salary <= 35000 | universitiy A)*P(universitiy A) / P(salary <= 35000)

= 0.8413*0.40 / 0.8818

= 0.3816

P(university A | salary <= 35000) = 0.3816

(please UPVOTE)

orchestra answered 11 months ago

Next > < Previous

Related Solutions

Suppose that salaries of recent graduates from a large state university are normally distributed with mean...

Suppose that salaries of recent graduates from a large state university are normally distributed with mean $45,000 and standard deviation $4,200. (1) What proportion of salaries are between $40,000 and $55,000? (2) What two salaries bound the middle 40%?

At a certain university, 40% of the students come from Orange County, 20% come from Los...

At a certain university, 40% of the students come from Orange County, 20% come from Los Angeles County, 20% come from another county in California, 10% come from another state, and 10% come from a different country. Zoe wants to see if the students in her class fit or do not fit this profile. She takes a sample: 100 come from Orange County, 35 come from Los Angeles County, 30 come from another county in California, 20 come from another...

A university surveyed recent graduates of the English Department for their starting salaries. Four hundred graduates...

A university surveyed recent graduates of the English Department for their starting salaries. Four hundred graduates returned the survey. The average salary was $25,000. The population standard deviation was $2,500. What is the 90% confidence interval for the mean salary of all graduates from the English Department? A) [$24,794, $25,206] B) [$24,988, $25,012] C) [$22,500, $27,500] D) [$24,755, $25,245]

A university surveyed recent graduates of the English department for their starting salaries. Three hundred graduates...

A university surveyed recent graduates of the English department for their starting salaries. Three hundred graduates returned the survey. The average salary was $25,000. The sample standard deviation was $1,500. What is the 95% confidence interval for the mean salary of all graduates from the English department?

1. Assume that the starting salaries for the Class of 2013 college graduates is (rounded, in...

1. Assume that the starting salaries for the Class of 2013 college graduates is (rounded, in $1000’s) normally distributed with µ = 45 and σ = 5. (Based on real data.) a. Sketch and label the normal curve. b. In what range must a starting salary be for a graduate to be in (approximately) the highest 16% ? c. In what range must a starting salary be for a graduate to be in (approximately) the lowest .15% ? d. In...

Lisa wants to determine if graduates from her college earn different incomes compared to graduates from...

Lisa wants to determine if graduates from her college earn different incomes compared to graduates from college in general. To test this, Lisa sends surveys to 1,000 graduates from her school and finds that the average income is $40,000 ( s = 5,000). If the average income is $45,000 for graduates in general, do graduates from Lisa's school differ significantly? Report the results in APA style and be sure to include information about effect size.

A Corporation receives 120 applications for positions from recent college graduates in POLS. Assume that 40%...

A Corporation receives 120 applications for positions from recent college graduates in POLS. Assume that 40% of these applicants are graduated from MIT. If they randomly select two application. What is the probability that one of them is MIT graduate?

Suppose college graduates earn $20 an hour and high school graduates earn $10 an hour. Suppose...

Suppose college graduates earn $20 an hour and high school graduates earn $10 an hour. Suppose too that the marginal product of college graduates at Johnson Tools is 5 hammers per hour, while the marginal product of high school graduates is 4 hammers per hour (regardless of the number of each type of worker employed). a. What is the least-cost production method for producing 100 hammers in an eight-hour day? Hire one-third college graduates and two-thirds high school graduates. Hire...

You are convinced that biology graduates from University X are smarter than chemistry graduates. What steps...

You are convinced that biology graduates from University X are smarter than chemistry graduates. What steps would you take to investigate this using the scientific method?

A University found that 27% of its graduates have taken an introductory statistics course. Assume that...

A University found that 27% of its graduates have taken an introductory statistics course. Assume that a group of 15 graduates have been selected. Compute the probability that from this group, there are exactly 2 graduates that have taken an introductory statistics course. Compute the probability that from this group, there are at most 3 graduates that have taken an introductory statistics course. Compute the probability that from this group, there are at least 4 graduates that have taken an...

Subjects