Question

In: Statistics and Probability

Weekly gross income earned by lecturers in XYZ University is normally distributed with a mean of...

Weekly gross income earned by lecturers in XYZ University is normally distributed with a mean of $1,600 and a standard deviation of $250. The Chief Operation Manager of XYZ University would like to do an audit on the weekly gross income earned by lecturers in his institution. Assist the manager is answering this: what is the probability that if 50 lecturers are randomly selected, their average weekly gross income would be more than $1,700?

a.

0.9954
b.

0.9977
c.

0.0023
d.

0.4977
e.

0.5023

Solutions

Expert Solution

Given that,

mean = = 1600

standard deviation = = 250

n=50

= =1600

= / n = 250/ 50 = 35.355

P( >1700 ) = 1 - P( < 1700)

= 1 - P[( - ) / < (1700-1600) /35.355 ]

= 1 - P(z <2.83 )

Using z table

= 1 - 0.9977

= 0.0023

orchestra answered 3 years ago
Next > < Previous

Related Solutions

Weekly gross income earned by lecturers in XYZ University is normally distributed with a mean of...
Weekly gross income earned by lecturers in XYZ University is normally distributed with a mean of $1,600 and a standard deviation of $250. The Chief Operation Manager of XYZ University would like to do an audit on the weekly gross income earned by lecturers in his institution. Assist the manager is answering this: what is the probability that if 50 lecturers are randomly selected, their average weekly gross income would be more than $1,700? a. 0.9954 b. 0.9977 c. 0.0023...
The weekly wages of steel workers at a steel plant are normally distributed with a mean...
The weekly wages of steel workers at a steel plant are normally distributed with a mean weekly wage of $940 and a standard deviation of $85. There are 1540 steel workers at this plant. a) What is the probability that a randomly selected steel worker has a weekly wage i) Of more than $850? ii) Between $910 and $960? b) What percentage of steel workers have a weekly wage of at most $820? c) Determine the total number of steel...
Suppose the scores earned on a statistics test are normally distributed with a mean of 65...
Suppose the scores earned on a statistics test are normally distributed with a mean of 65 and a standard deviation 8. The instructor wants to curve the test scores as follows: The top 5% get an A, the next 20% get a B, the middle 50% get a C, the bottom 10% get an F, and the rest earn a D. Determine the score cutoffs for the test.
The heights of female students in a university are approx normally distributed with a mean of...
The heights of female students in a university are approx normally distributed with a mean of 162 cm and a standard dev of 8 cm. Explain your answers. a) Approx 68% of all female students in a university will have heights between ____ cm and ____ cm. b) Heights greater than ____ cm would be considered peculiar.
The weight of male students at a certain university is normally distributed with a mean of...
The weight of male students at a certain university is normally distributed with a mean of 175 pounds with a standard deviation of 7.6 pounds. Find the probabilities. 1. A male student weighs at most 186 pounds. 2. A male students weighs at least 160 pounds. 3. A male student weighs between 165 and 180 pounds. Please show work. Ideally excel commands would be helpful, but anything would be great!
Weekly demand for electric motors at a Japanese motor manufacturer is normally distributed, with a mean...
Weekly demand for electric motors at a Japanese motor manufacturer is normally distributed, with a mean of 1,000 and a standard deviation of 1,000. Motors are currently assembled in China and delivered at a cost of 20,000 yen/motor. The supplier takes eight weeks to supply an order. A local Japanese manufacturer has offered to deliver motors with a lead time of one week at a cost of 20,400 yen per motor. The motor manufacturer monitors its inventory continuously. The manufacturer...
The SAT scores earned on the math portion are approximately normally distributed with mean 516 and...
The SAT scores earned on the math portion are approximately normally distributed with mean 516 and standard deviation 116. Answer the following questions based on this information. Make sure you show your work. 1. Using a printout of the graph above or making your own copy, mark the mean SAT score on the math proportion at the appropriate place. Then mark values of score that are 1, 2, and 3 standard deviations away from the mean value. Labeling your marks...
Test scores on a university admissions test are normally distributed, with a mean of 500 and...
Test scores on a university admissions test are normally distributed, with a mean of 500 and a standard deviation of 100. d. 20% of test scores exceed what value? i know P(X>= c-500/100) = .20 but after this, i dont understand why c -500/100 =.84 where did this .84 come from?
Same problem statement: Weekly demand for DVD-Rs at a retailer is normally distributed with a mean...
Same problem statement: Weekly demand for DVD-Rs at a retailer is normally distributed with a mean of 1,000 boxes and a standard deviation of 150. Currently, the store places orders to the supplier, with a reorder point of 4,200 boxes. The order quantity to the supplier is fixed at 5,000 boxes. Replenishment lead time is 4 weeks, fixed order cost per order is $100, each box costs the retailer $10, and the inventory holding cost is 25% per year. Under...
The number of pizzas consumed per month by university students is normally distributed with a mean...
The number of pizzas consumed per month by university students is normally distributed with a mean of 10 and a standard deviation of 3. A. What proportion of students consume more than 12 pizzas per month? Probability = B. What is the probability that in a random sample of size 8, a total of more than 72 pizzas are consumed? (Hint: What is the mean number of pizzas consumed by the sample of 8 students?) Probability =
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT