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Lecture notes of 12 pages for the course Statistics at UCalgary (Statiscics examples)
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Benjamin Odei F2021STAT213Assignment 7 is due on Thursday, December 09, 2021 at 11:59pm.
The number of attempts available for each question is noted beside the question. If you are having trouble figuring out your error, you
should consult the textbook, or ask a fellow student, one of the TA’s or your professor for help.
There are also other resources at your disposal, such as the Mathematics Continuous Tutorials. Don’t spend a lot of time guessing – it’s
not very efficient or effective.
Make sure to give lots of significant digits for (floating point) numerical answers. For most problems when entering numerical answers,
you can if you wish enter elementary expressions such as 2 ∧ 3 instead of 8, sin(3 ∗ pi/2)instead of -1, e ∧ (ln(2)) instead of 2, (2 +
tan(3)) ∗ (4 − sin(5)) ∧ 6 − 7/8 instead of 27620.3413, etc.
Problem 1. (1 point) Problem 2. (1 point)
You have information to suggest that a certain continuous variable You are interested in finding out the mean number of customers
of a population has a mean of µ = 13.73 and a standard deviation entering a 24-hour convenience store every 10-minutes. You sus-
of σ = 4.31. You are to randomly pick n = 79 individuals from pect this can be modeled by the Poisson distribution with a a
this population and observe the value of the population variable mean of λ = 4.21 customers. You are to randomly pick n = 76
on each . This value is to measured as Xi . 10-minute time frames, and observe the number of customers
who enter the convenience store in each. After which, you are to
After the random sample of n = 79 has been taken, you are asked average the 76 counts you have. That is, compute the value of X.
to consider the behavior of the statistic X.
(a) What can you expect the value of X to be?
(a) Complete the statement below. Use as many decimals as you
can. Enter your answer using all the decimals you can.
The distribution of X
•? (b) Find the value of the standard deviation of X. Enter your
• is approximately Normal answer using all the decimals you can.
• is exactly Normal
• is skewed to the right σX =
• has an unknown shape
with a mean µX = and a standard deviation σX =
(c) Find the probability that mean of the sample of 76 is between
1.8 and 4.3. If rounding only round once, at the end do not round
before that. Ensure you use at least four decimals in your z-values.
(b) Find the probability that mean of the sample of n = 79 is
between 12.93 and 14.23. Use at least four decimals in your z-
P(1.8 ≤ X ≤ 4.3) = Use at least four decimals in your
values, and enter your answer to at least four decimals.
answer.
(d) 90% of the time, the observed value of X will exceed what
value?
Answer(s) submitted:
•
(use at least four decimals in your answer)
•
•
•
Answer(s) submitted:
(incorrect)
•
•
•
•
(incorrect)
1
, Problem 3. (1 point) Problem 4. (1 point)
Once checked in at the ticket kiosk, the amount of time it takes You are to roll a fair die n = 105 times, each time observing the
a airline passenger at the Calgary International Airport to clear number of dots appearing on the topside of the die. The number
security is a random variable that can be modeled by the Expo- of dots showing on the topside of toss i is a random variable rep-
nential distribution with a µ = 41.9 minutes. resented by Xi , i = 1, 2, · · · , 105.
A statistician is randomly select n = 32 airline passengers and
record how long, in minutes, it takes each to clear security once (a) Consider the distribution of the random variable Xi . Find the
each has checked in at the ticket kiosk. mean and the standard deviation of the number of dots showing
on the uppermost face of a single roll of this die.
(a) Complete the statement below. Enter your answer using all µXi = Enter your answer using all the decimals you can.
the decimals you can.
σXi = Enter your answer using all the decimals you can.
The distribution of X
•?
• is approximately Normal (b) Now think about the average of your n = 105 tosses of the
• is exactly Normal fair die. What can you say about the distribution of this average?
• is skewed to the right Complete the sentence, Enter your answer using all the decimals
• is Exponential you can.
• is Poisson
• has an unknown shape The distribution of X
•?
with a mean µX = minutes and a standard deviation σX =
minutes. • is approximately Normal
• is exactly Normal
• is skewed to the right
(b) What is the probability that the average time for this sample of • is Uniform
n = 32 airline passengers to clear security is between 27 minutes • has an unknown shape
and 58 minutes? Enter your answer using all the decimals you can. with a mean µX = and a standard deviation σX =
(c) What is the probability that the average topside on your
n = 105 tosses will be somewhere between 3.3 and 3.7? Enter
(c) 95% of the time, the mean time it takes n = 32 airline pas- your answer using all the decimals you can.
sengers to clear security after ticket kiosk check-in is at most how
many minutes? Enter your answer using all the decimals you can.
minutes
(d) What is the probability that the average of your n = 105 tosses
is greater than 4.2? Enter your answer using all the decimals you
Answer(s) submitted: can.
•
•
•
•
• Answer(s) submitted:
(incorrect) •
•
•
•
•
•
•
2
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