Tim was given a large bag of sweets and ate one third of the sweets before stopping as he was feeling sick. The next day he ate
1 answer:
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Answer:
Step-by-step explanation:
Given that a fisherman catches fish according to a Poisson process with rate lambda = 0.6 per hour.
The fisherman will keep fishing for two hours.
Since he continues till he gets atleast one fish, we can calculate probability as follows:
(a) Find the probability that he stays for more than two hours.
= Prob (x=0) in I two hours and P(X≥1) in 3rd hour
=P(x=0)*P(X=0)*P(X≥1) (since each hour is independent of the other)
=
(b) Find the probability that the total time he spends fishing is between two and five hours.
Prob that he does not get fish in I two hours * prob he gets fish between 3 and 5 hours
=
(c) Find the expected number offish that he catches.
Expected value in Geometric distribution = , where p = prob of getting 1 fish in one hour
=
(d) Find the expected total fishing time, given that he has been fishing for four hours.
= Expected fishing time total/expected fishing time for 4 hours
=3/0.6*4
= 1.25 hours
Answer:
1) n=48
2) n=298
3) n=426
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
represent the real population proportion of interest
represent the estimated proportion for the sample
n is the sample size required (variable of interest)
represent the critical value for the margin of error
The population proportion have the following distribution
Part 1
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by and
. And the critical value would be given by:
The margin of error for the proportion interval is given by this formula:
(a)
And on this case we have that and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b)
We can assume that the estimated proportion is 0.23 for the 25 to 30 group. And replacing into equation (b) the values from part a we got:
And rounded up we have that n=48
Part 2
The margin of error on this case changes to 0.04 so if we use the same formula but changing the value for ME we got:
And rounded up we have that n=298
Part 3
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by and
. And the critical value would be given by:
The margin of error for the proportion interval is given by this formula:
(a)
And on this case we have that and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b)
We can assume that the estimated proportion is 0.23 for the 25 to 30 group. And replacing into equation (b) the values from part a we got:
And rounded up we have that n=426