Each year a nationally recognized publication conducts its 'Survey of America's Best Graduate and Professional Schools.' An acad
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Answer:
(a) The fraction of employees is 0.84.
(b)
(c)
(d) No. The left part of the distribution would be truncated too much.
Step-by-step explanation:
(a) If the weekly salaries are normally distributed, estimate the fraction of employees that make more than $300 per week.
We have to calculate the z-value and compute the probability
(b) If every employee receives a year-end bonus that adds $100 to the paycheck in the final week, how does this change the normal model for that week?
The mean of the salaries grows $100.
The standard deviation stays the same ($450)
(c) If every employee receives a 5% salary increase for the next year, how does the normal model change?
The increases means a salary X is multiplied by 1.05 (1.05X)
The mean of the salaries grows 5%, to $787.5.
The standard deviation increases by a 5% ($472.5)
(d) If the lowest salary is $300 and the median salary is $525, does a normal model appear appropriate?
No. The left part of the distribution would be truncated too much.
The area of the ellipse is given by
To use Green's theorem, which says
( denotes the boundary of
), we want to find
and
such that
and then we would simply compute the line integral. As the hint suggests, we can pick
The line integral is then
We parameterize the boundary by
with . Then the integral is
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Notice that kind of resembles the equation for a circle with radius 4,
. We can change coordinates to what you might call "pseudo-polar":
which gives
as needed. Then with , we compute the area via Green's theorem using the same setup as before:
Given:
Seventy cards are numbered 1 through 70, one number per card. One card is randomly selected from the deck.
To find:
The probability that the number drawn is a multiple of 3 and a multiple of 5.
Solution:
Total number from 1 to 70 = 70
Multiple of 3 from 1 to 70 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69.
Multiple of 5 from 1 to 70 are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70.
Numbers which are multiply of both number 3 and 5 = 15, 30, 45, 60
Number of favorable outcomes = 4
Therefore, the required probability is .