(4) Annual rainfall over the slopes of southern Himalayan mountains has varied from 750mm to 1250mm over the lastseveral hundred years. If the distribution of the amount of annual rainfall has mean u = 1000mm and standarddeviation o = 100mm, what is the likelihood that the average rainfall over the last ten years could have been below800mm, in the absence of any climate change?Solve this problem by taking the following four steps one by one.Step (i). We need to compute P(X 10 < 800). where X 10 is the average over the ten years of rainfall. Can we computethis probability exactly:(a) No, the population distribution is not known.(b) Yes, since the population distribution is Poisson.(c) Yes, since the population distribution is Binomial.(d) No, because no matter what the population distribution may be, it is always impossible to find the exact distributionof X 10-(e) None of the above.(a)(b)(c)(d)(e)N/A(i- Select One)Step (ii). An approximation to the probability, P(X 10 < 800), is P(Z < –6.32), where Z ~N(0, 1). WHY:TTVGCVFCLTCBSNone of the aboveN/A(ii- Select One)Step (iii). Consulting a standard normal table or otherwise what is an approximate value of P(Z < -6.32):-1 0 11/2None of the aboveN/A(iii- Select One)Step (iv). What assumptions did you make and what conclusions can you draw?(a) No assumptions were made, and the conclusion is that perhaps the climate has changed or a prolonged dryer spell isin effect.(b) The CLT is applicable and the conclusion is that perhaps the climate has changed or a prolonged dryer spell is ineffect.(c) No assumptions were made, and this is part of the normal weather cycle(d) The CLT is applicable, and this is part of the normal weather cycle(e) None of the above(a)(b)(c)(d)(e)N/A(iv- Select One)

(i). Option D (ii). option c (iii.) Option b

of X 10. (e) None of the above. (a) (b) (c) (d) (e) N/A (i- Select One) Step (ii). An approximation to the probability, P(X 10 < 800), is P(Z < -6.32), where Z ~ N(0, 1). WHY? TTV GCVF CLT CBS None of the above N/A (ii- Select One) Step (iii). Consulting a standard normal table or otherwise what is an approximate value of P(Z < -6.32)? -1 0 1 1/2 None of the above N/A (iii- Select One) Step (iv). What assumptions did you make and what conclusions can you draw: (a) No assumptions were made, and the conclusion is that perhaps the climate has changed or a prolonged dryer spell is in effect. (b) The CLT is applicable and the conclusion is that perhaps the climate has changed or a prolonged dryer spell is in effect. (c) No assumptions were made, and this is part of the normal weather cycle (d) The CLT is applicable, and this is part of the normal weather cycle (e) None of the above (a) (b) (c) (d) (e) N/A (iv- Select One)

of X 10. (e) None of the above. (a) (b) (c) (d) (e) N/A (i- Select One) Step (ii). An approximation to the probability, P(X 10 < 800), is P(Z < -6.32), where Z ~ N(0, 1). WHY? TTV GCVF CLT CBS None of the above N/A (ii- Select One) Step (iii). Consulting a standard normal table or otherwise what is an approximate value of P(Z < -6.32)? -1 0 1 1/2 None of the above N/A (iii- Select One) Step (iv). What assumptions did you make and what conclusions can you draw: (a) No assumptions were made, and the conclusion is that perhaps the climate has changed or a prolonged dryer spell is in effect. (b) The CLT is applicable and the conclusion is that perhaps the climate has changed or a prolonged dryer spell is in effect. (c) No assumptions were made, and this is part of the normal weather cycle (d) The CLT is applicable, and this is part of the normal weather cycle (e) None of the above (a) (b) (c) (d) (e) N/A (iv- Select One)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!

Question

100%

(4) Annual rainfall over the slopes of southern Himalayan mountains has varied from 750mm to 1250mm over the last
several hundred years. If the distribution of the amount of annual rainfall has mean u = 1000mm and standard
deviation o = 100mm, what is the likelihood that the average rainfall over the last ten years could have been below
800mm, in the absence of any climate change?
Solve this problem by taking the following four steps one by one.
Step (i). We need to compute P(X 10 < 800). where X 10 is the average over the ten years of rainfall. Can we compute
this probability exactly:
(a) No, the population distribution is not known.
(b) Yes, since the population distribution is Poisson.
(c) Yes, since the population distribution is Binomial.
(d) No, because no matter what the population distribution may be, it is always impossible to find the exact distribution
of X 10-
(e) None of the above.
(a)
(b)
(c)
(d)
(e)
N/A
(i- Select One)
Step (ii). An approximation to the probability, P(X 10 < 800), is P(Z < –6.32), where Z ~
N(0, 1). WHY:
TTV
GCVF
CLT
CBS
None of the above
N/A
(ii- Select One)
Step (iii). Consulting a standard normal table or otherwise what is an approximate value of P(Z < -6.32):
-1 0 1
1/2
None of the above
N/A
(iii- Select One)
Step (iv). What assumptions did you make and what conclusions can you draw?
(a) No assumptions were made, and the conclusion is that perhaps the climate has changed or a prolonged dryer spell is
in effect.
(b) The CLT is applicable and the conclusion is that perhaps the climate has changed or a prolonged dryer spell is in
effect.
(c) No assumptions were made, and this is part of the normal weather cycle
(d) The CLT is applicable, and this is part of the normal weather cycle
(e) None of the above
(a)
(b)
(c)
(d)
(e)
N/A
(iv- Select One)

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