SOLUTION: I am desperate! please help!
The average salary for graduates entering the actuarial field is $40,000 ( ). If the salaries are normally distributed with a standard deviation of
Algebra.Com
Question 921812: I am desperate! please help!
The average salary for graduates entering the actuarial field is $40,000 ( ). If the salaries are normally distributed with a standard deviation of $5000 (σ = 5000), find the probability that:
a. An individual graduate (n = 1) will have a salary over $45,000: P(X > 45,000).
b. A group of nine graduates (n = 9) will have an average over $45,000: P( )
c. A group of nine graduates (n = 50) will have an average over $45,000: P( )
d. A group of nine graduates (n = 125) will have an average over $45,000: P( )
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
For normal distributions we use z-value to determine probabilities (Pr),
we are given that the mean is 40000 and standard deviation is 5000
a) Pr(X>45000) = 1 - Pr(X<45000)
calculate the z-value = (45000 - 40000) / 5000 = 1, consult z-tables
Pr(X<45000) = 0.8413
Pr(X>45000) = 1 - 0.8413 = 0.1587
b) with a sample space of 9 students, we calculate a new standard deviation
sample standard deviation = standard deviation / square root (n)
sample standard deviation = 5000 / square root (9) = 1666.666666667
Pr(X>45000) = 1 - Pr(X<45000)
calculate the z-value = (45000 - 40000) / 1666.666666667 = 3 , consult z-tables
Pr(X<45000) = 0.9987
Pr(X>45000) = 1 - 0.9987 = 0.0013
c)n = 50, for n > 40 use the population standard deviation
sample standard deviation = 5000
calculate the z-value = (45000 - 40000) / 5000 = 1 , consult z-tables
Pr(X>45000) = 1 - 0.8413 = 0.1587
d) n = 125, for n > 40 use the population standard deviation
sample standard deviation = 5000
calculate the z-value = (45000 - 40000) / 5000 = 1 , consult z-tables
Pr(X>45000) = 1 - 0.8413 = 0.1587
RELATED QUESTIONS
4.) The average salary for graduates entering the actuarial field is $40.000. If the... (answered by stanbon)
The average salary for
graduates entering the actuarial field is $40,000. If the... (answered by Boreal)
The average salary for graduates entering the actuarial field is $40,000. If the salaries (answered by Theo)
The average salary of graduates entering the actuarial field is reported to be $40,000.... (answered by stanbon)
8. The average salary of graduates entering the actuarial field is reported to be... (answered by stanbon)
The average salary of graduates entering the actuarial field is reported to be $40,000.... (answered by Boreal)
3. The recent average starting salary for new college graduates in computer information... (answered by ikleyn)
Please help. I am having a hard time figuring this out. The book is Statstics for... (answered by stanbon)
a) The average salary of graduates entering the actuarial field is reported to be $40,000 (answered by Boreal)