Fundamentals of Statistics and Probability Assignment: Answers

MTH219 Fundamentals of Statistics and Probability

Answer to question 1:
1[a]
Here, total number of rating = 400
Therefore, top 15% = 400*15% = 60
As per given information, 12 rating has been chosen from these 60 rating.
[i] Therefore, the probability that the chosen rating will be the highest rating = 12C1 / 60C1
= 12/60 = 1/5
[ii] Therefore, the probability that the chosen rating will be the lowest rating = 12C1 / 60C1
= 12/60 = 1/5
1[b]
Here, the probability of Type A = 0.03
Probability of Type B = 0.02
And probability of both Type A and Type B = 0.004
Hence, Probability of Type B given Type A is occurred = 0.004/0.03 = 0.13333
1[c]
Greater Than 70 Less than 70 Total
Dolomit
e 55 425 480
Shale 255 15 270
310 440 750
If we define A as the event that Dolomite is there and B is the even as the Gamma ray reading
is more than 70 API units, then
P(A) = 480/750 = 0.64
P(Ac) = 270/750 = 0.36
P(B/A) = 55/480 = 0.11458
P(B/Ac)=255/270 = 0.94444

Therefore, P(A/B) =
P ( B
A )∗P ( A )
P ( B
A )∗P ( A ) + P ( B
Ac )∗P ( Ac )
=0.11458*0.64/(0.11458*0.64+0.9444*0.36)
= 0.177419355
Since, the probability is 17.74%, they should mine.
1[d]
Here, λ = 1/8
Since, the event is following exponential distribution, it can be said that
P(X>11)
= 1-P(X<=11)
= 1 – (1/8)*e^(-(1/8))*11
= 0.031604949
1[e]
Here, probability = 1/1000 = 0.001.
[i] it will follow binomial distribution. Hence,
= P(X<4)
=P(X =0) + P(X=1) + P(X=2) + P(X=3)
= 5000!/(0!*(5000-0)!)*p^(0)*(1-p)^(5000-0) + 5000!/(1!*(5000-1)!)*p^(1)*(1-p)^(5000-1)
+ 5000!/(2!*(5000-2)!)*p^(2)*(1-p)^(5000-2) + 5000!/(3!*(5000-3)!)*p^(3)*(1-p)^(5000-3)
= 0.264885
[ii] It will follow Poisson distribution
Hence, λ =(1/1000)*5000 = 5.
So, = P(X<4)
=P(X =0) + P(X=1) + P(X=2) + P(X=3)