Question

In: Statistics and Probability

The GPA of accounting students in a university is known to be normally distributed. A random...

The GPA of accounting students in a university is known to be normally distributed. A random sample of 31 accounting students results in a mean of 3.14 and a standard deviation of 0.15. Construct the 99% confidence interval for the mean GPA of all accounting students at this university.

Solutions

Expert Solution

Solution :

Given that,

Point estimate = sample mean = = 3.14

Population standard deviation =    = 0.15
Sample size = n =31

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576   ( Using z table )

Margin of error = E = Z/2* ( /n)

= 2.576 * ( 0.15/ 31)

= 0.069

At 99% confidence interval is,

- E < < + E

3.14-0.069 < < 3.14+0.069

3.071< < 3.209


Related Solutions

The GPA of accounting students in a university is known to be normally distributed. A random...
The GPA of accounting students in a university is known to be normally distributed. A random sample of 32 accounting students results in a mean of 2.64 and a standard deviation of 0.15. Construct the 95% confidence interval for the mean GPA of all accounting students at this university.
Assume that the GPA of MBA students at Boston University is normally distributed with µ =...
Assume that the GPA of MBA students at Boston University is normally distributed with µ = 3.3 and σ = .2. If we sample 16 of the MBA students what is the probability that the average GPA will exceed 3.36?
The GPA of graduating engineering students in the fictitious Kingdom of Statistans approximately normally distributed with...
The GPA of graduating engineering students in the fictitious Kingdom of Statistans approximately normally distributed with a mean of 3.1 and a standard deviation of 0.2. The starting salary in Statistan is decided by the central government to be exactly $35K + $2.5K times the square of the GPA. (a) What GPAs and salaries do the top 20% of graduating students have? (b) What are the expected value and standard dev. of the starting salary? (c) What’s the ranking of...
A random sample of 40 students taken from a university showed that their mean GPA is...
A random sample of 40 students taken from a university showed that their mean GPA is 2.94 and the standard deviation of their GPAs is .30. Construct a 99% confidence interval for the mean GPA of all students at this university
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!
5.4 GPA is approximately normally distributed for all students that have been accepted to UCLA. The...
5.4 GPA is approximately normally distributed for all students that have been accepted to UCLA. The average gpa is 4.0 with standard deviation of .2. 50 students were sampled and asked, "what is your gpa?": a) Calculate the probability the mean gpa is 3.95 or lower b) Calculate the standard deviation for the sampling distribution. b) Between what 2 gpa's are considered normal for being accepted at UCLA c) What gpa represents the top 10% of all students d) What...
GPA is approximately normally distributed for all students that have been accepted to UCLA. The average...
GPA is approximately normally distributed for all students that have been accepted to UCLA. The average gpa is 4.0 with standard deviation of .2. a) What % of admitted students had a gpa lower than 3.5. b)What percent had a gpa above 4.1 c)What gpa represents the top 10% of all students
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 =
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 8 and a standard deviation of 2. Use Excel to answer the following questions: A. What proportion of students consume more than 11 pizzas per month? Probability = B. What is the probability that in a random sample of size 8, a total of more than 80 pizzas are consumed? (Hint: What is the mean number of pizzas consumed by the sample of...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT