Mathematics, 24.10.2019 16:43, kaitlynbrace4214

Use r/excel to simulate 1000 normal random numbers with mean 0.5 and standard deviation 0.6. record the sample mean and sample variance of these 1000 simulated random numbers. 1 (b) simulate a random number u that is uniformly distributed between 0 and 1, record its value and write it down: (c) calculate the probability that x ∼ n (0.5, 0.6 2 ) is larger than u obtained in (b). (d) use these 1000 normal random numbers obtained in (a) to find an approximate answer to (c), record its value and write it down: (e) designing a simulation procedure to more accurately approximate p(x > u). (f) find out that x is smaller than which number with probability u (note u is between 0 and 1 and hence can be treated as a probability). (g) using these 1000 normal random numbers obtained in (a) to find an approximate answer to (f), record its value and write it down: (h) given the 1000 random numbers obtained in (a), provide your 95% confidence interval of the true mean of the probability distribution that these 1000 random numbers are simulated from. (i) to reduce the width of the 95% confidence interval of the true mean in (h) by about 50%, how many more random samples from the underlying distribution are needed? (j) simulate these additional random numbers and combing them with the original 1000 random numbers to find the sample mean and sample variance, and provide your updated 95% confidence interval of the true mean.

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answered: Guest

you never say the total so we cant find the percentage used for petrol

step-by-step explanation:

answered: Guest

your exact question is kind of difficult to understand, so maybe an example will explain what you're supposed to do? i'll work through the first problem on the worksheet.

suppose you have a tray of 652 brownies, and you have 5 friends that you want to feed without picking favorites. how many brownies can you dole out to each of your friends in equal amounts? how many will be left over for you to eat?

what you're doing here is finding a way to arrange the number 652 as the sum of integer multiple of 5 and some remainder: $652=5q+r$

here $q$ ("q" for quotient) is the number of brownies each of your friends get, and $r$ is the remainder. that's the basic idea behind division.

we break up the number 652 into parts so that the leading digit stands on its own:

652 = 600 + 52

first we check if it's possible to hand out exactly 100 brownies to each friend. with 5 friends, this means we want to know if we can take out 500 brownies from the tray. we can do this 1 time because we have 600 brownies to take from, and when we do that we're left with 100 + 52 brownies to divvy up. so we know that

652 = 1*500 + 152

next we want to know if it's possible to hand out exactly 10 brownies per friend. if we can, we have to remove 50 brownies from the tray each time until we can't. we have 152 brownies left, and we know that 3(50) = 150, so

152 = 3*50 + 2

now we have 2 brownies left in the tray. is it possible to hand 1 out to each of your 5 friends? no, you'd need a minimum of 5 brownies to do that. so the last 2 are yours.

putting everything together, we found that

652 = 1*500 + 3*50 + 2

and we can rearrange this to write

652 = 5*100 + 5*30 + 2

652 = 5(100 + 30) + 2

652 = 5*130 + 2

so $q=130$ and $r=2$ .

you might be more accustomed to the table depicting the algorithm. that's just a compact way of organizing what we've done above. you can consult the image i've attached below.

answered: Guest

the value of x is 9 ⇒ answer b

step-by-step explanation:

* we can solve this problem using cosine and sine rule

- in δ abc

∵ ab = 36 , bc = 28 , ac = 16

- lets find the measure of angle b using the cosine rule

∵ cos b = [ab² + bc² - ac²]/2(ab)(bc)

∴ cos b = [36² + 28² - 16²]/2(36)(28)

∴ cos b = 19/21

∴ m∠b = cos^-1(19/21) ≅ 25°

- lets find the measure of angle a using the sine rule