The student will calculate probabilities using the Central Limit Theorem.
Given
Yoonie is a personnel manager in a large corporation. Each month she must review 16 of the employees. From past experience, she has found that the reviews take her approximately 4 hours each to do with a population standard deviation of 1.2 hours. Let
be the random variable representing the time it takes her to complete one review. Assume
is normally distributed. Let
be the random variable representing the mean time to complete the 16 reviews. Let
be the total time it takes Yoonie to complete all of the month’s reviews. Assume that the 16 reviews represent a random set of reviews.
Distribution
Complete the distributions.
~
~
~
Graphing probability
For each problem below:
Sketch the graph. Label and scale the horizontal axis. Shade the region corresponding to the probability.
Calculate the value.
Find the probability that
one review will take Yoonie from 3.5 to 4.25 hours.
________
________
_______
3.5, 4.25, 0.2441
Find the probability that the
mean of a month’s reviews will take Yoonie from 3.5 to 4.25 hrs.
_______
0.7499
Find the 95th percentile for the
mean time to complete one month’s reviews.
The 95th Percentile=
4.49 hours
Find the probability that the
sum of the month’s reviews takes Yoonie from 60 to 65 hours.
The Probability=
0.3802
Find the 95th percentile for the
sum of the month’s reviews.
The 95th percentile=
71.90
Discussion question
What causes the probabilities in
[link] and
[link] to differ?
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form