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EDIT:These are all the questions that I do not know how to do. Thank you for helping!

1)Given that D~B(12, 0.7), calculate

b)the smallest value of d such that P(D>d)<0.90

2)Joseph and four friends each have an independent probability 0.45 of winning a prize. Find the probability that

a)exactly two of the friends win a prize(I have answered this)

b)Joseph and only one friend win a prize

3)

a)A fair coin is tossed 8 times. Calculate the probability that the first 4 tosses and the last 4 tosses result in the same number of heads.

b)Two teams each consist of 3 players. Each player is in a team tosses a fair coin once and the team's score is the total number of heads thrown. Find the probability that the teams have the same score.

5)Show that, when two fair dice are thrown, the probability of obtaining a 'double' is 1/6, where a 'double' is defined as the same score on both dice. Four players play a board game which requires them to take it in turns to throw two fair dice. Each player throws the two dice once in each round. When a 'double' is thrown the player moves forward six squares. Otherwise the player moves forward one square. Find

a)the probability that the first double occurs on the third throw of the same,

b)the probability that exactly one of the four players obtains a 'double' in the first round,

c)the probability that a 'double' occurs exactly once in 4 of the first 5 rounds.

6)Six hens are observed over a period of 20 days and the number of eggs laid each day is summarised in the following table.

Number of eggs 3 4 5 6

Number of days 2 2 10 6

State the probability that a randomly chosen hen lays an egg on a given day.

Calculate the expected frequencies of 3, 4, 5, and 6 eggs.

Normal Distribution

8)The packets in which sugar is sold are labelled '1 kg packets'. In fact the mass of sugar in a packet is distributed normally with mean mass 1.08 kg.

Smpling of packets of sugar shows that just 2.5% are 'underweight' (that is, contain less than the stated mass of 1 kg).

Find the standard deviation of the distribution.

10)The random variable X has a bormal distribution. The mean is a (where a>0)and the variance is 0.25a^2.

a)Find P(X>1.5a)

1)Given that D~B(12, 0.7), calculate

b)the smallest value of d such that P(D>d)<0.90

2)Joseph and four friends each have an independent probability 0.45 of winning a prize. Find the probability that

a)exactly two of the friends win a prize(I have answered this)

b)Joseph and only one friend win a prize

3)

a)A fair coin is tossed 8 times. Calculate the probability that the first 4 tosses and the last 4 tosses result in the same number of heads.

b)Two teams each consist of 3 players. Each player is in a team tosses a fair coin once and the team's score is the total number of heads thrown. Find the probability that the teams have the same score.

5)Show that, when two fair dice are thrown, the probability of obtaining a 'double' is 1/6, where a 'double' is defined as the same score on both dice. Four players play a board game which requires them to take it in turns to throw two fair dice. Each player throws the two dice once in each round. When a 'double' is thrown the player moves forward six squares. Otherwise the player moves forward one square. Find

a)the probability that the first double occurs on the third throw of the same,

b)the probability that exactly one of the four players obtains a 'double' in the first round,

c)the probability that a 'double' occurs exactly once in 4 of the first 5 rounds.

6)Six hens are observed over a period of 20 days and the number of eggs laid each day is summarised in the following table.

Number of eggs 3 4 5 6

Number of days 2 2 10 6

State the probability that a randomly chosen hen lays an egg on a given day.

Calculate the expected frequencies of 3, 4, 5, and 6 eggs.

Normal Distribution

8)The packets in which sugar is sold are labelled '1 kg packets'. In fact the mass of sugar in a packet is distributed normally with mean mass 1.08 kg.

Smpling of packets of sugar shows that just 2.5% are 'underweight' (that is, contain less than the stated mass of 1 kg).

Find the standard deviation of the distribution.

10)The random variable X has a bormal distribution. The mean is a (where a>0)and the variance is 0.25a^2.

a)Find P(X>1.5a)

Are you gonna share your thoughts on any of these or do you just expect people to do your homework for you without so much as a thank you?

I do not expect people to give me the answers but help me in understanding them or giving me some hints. Sorry that I didn't state here that these are all the questions that I do not know how to do in the A-level Statistic book which endorsed by CIE. I have tried them but either couldn't understand them or be able to get the right answers so I am here to seek for help.

Also, it's not my homework I am doing a lot of questions because my exam is on November 2nd. Hope you understand.

Thanks for helping.

Also, it's not my homework I am doing a lot of questions because my exam is on November 2nd. Hope you understand.

Thanks for helping.

authecroix123

I do not expect people to give me the answers but help me in understanding them or giving me some hints. Sorry that I didn't state here that these are all the questions that I do not know how to do in the A-level Statistic book which endorsed by CIE. I have tried them but either couldn't understand them or be able to get the right answers so I am here to seek for help.

Also, it's not my homework I am doing a lot of questions because my exam is on November 2nd. Hope you understand.

Thanks for helping.

Also, it's not my homework I am doing a lot of questions because my exam is on November 2nd. Hope you understand.

Thanks for helping.

Although I don't object to helping, which you know from my previous posts on your other thread, I don't think this is the best way to do it. I mean, you can look through them and understand and all that, but it's different when you actually do it yourself, so I strongly suggest you try each of them out and we'll correct you or guide you (if we have time). I mean, at least look like you even attempted some of them. I really don't believe that you can't do one single question.

zhang

Although I don't object to helping, which you know from my previous posts on your other thread, I don't think this is the best way to do it. I mean, you can look through them and understand and all that, but it's different when you actually do it yourself, so I strongly suggest you try each of them out and we'll correct you or guide you (if we have time). I mean, at least look like you even attempted some of them. I really don't believe that you can't do one single question.

Please understand that I have done all the questions in the books except the questions I posted here. These are all the questions that I don't know how to do as I have stated. I tried and thought of them but couldn't get the right answers.

Question 1

If it asked to find the probability then I know how to find it, but now it asks for the smallest value of d which I do not know how to find it.

Question 2

I have answered part a

For part 2, I am confused because it asks for "Joseph and one friend" which makes me confused. If it was like part a, which didn't say one of the persons is Joseph" but this question does. So I do not know how to do it.

Question 3

Both questions confuse me.

Question 4

I have cleared this.

Question 5

I now know for part a but still do not get part b and c.

Question 6

Mean = [(3x2)+(4x2)+(5X10)+(6x6)] / 20

= 5

I do not know for the rest part.

Question 7

I don't know what is meant by " in boxes of 10". Is it the same as "in 10 boxes"? I also don't know how to do this question.

Question 8

Mean is 1.08, we want to find standard deviation.

But we don't know the value of x in P(X<x), how do we find it?

Question 9

Find the possibility that X has a negative value.

Mean is 3 and Standard deviation is 2. So is it P(X<0) or P(X <_-1)? Which one should we use?

Question 10

Mean=a, a >0 , variance=0.25a^2, so is Standard deviation 0.25a?

For part a, P(X>1.5a) = P[Z> (1.5a - a) / 0.25a]

= P(Z> 2)

= 1 - 0.9772

=0.0228 but it's wrong(the answer is 0.1587)

For part b, what is the value x we should use?

authecroix123

9)The random variable X can take negative and positive values. X is distributed normally with mean 3 and variance 4. Find the possibility that X has a negative value.

9)The random variable X can take negative and positive values. X is distributed normally with mean 3 and variance 4. Find the possibility that X has a negative value.

ALright so mean=3 and variance=4. Since the standard deviation is the square root of the variance, it equals 2.

Thus you do z= (0-3)/2= -1.5= (X-M)/S

Now the area from negative infinity to -1.5 is the probability that X is negative.

Thus use your TI-89/86/83 calculator or a graph to see what the p-value is: normcdf(-infinity,-1.5)

They should have the areas on a chart for you.

authecroix123

Expectation and Variance of a random variable

7)Some of the eggs sold in a store are packed in boxes of 10. For any egg, the probability that it is cracked is 0.05, indepedently of all other eggs. A shelf contains 80 of these boxes. Calculate the expected value of all other eggs. A shelf contains 80 of these boxes. Calculate the expected value of the number of boxes on the shelf which do not contain a cracked egg.

Expectation and Variance of a random variable

7)Some of the eggs sold in a store are packed in boxes of 10. For any egg, the probability that it is cracked is 0.05, indepedently of all other eggs. A shelf contains 80 of these boxes. Calculate the expected value of all other eggs. A shelf contains 80 of these boxes. Calculate the expected value of the number of boxes on the shelf which do not contain a cracked egg.

EV of the number of eggs not cracked on the shelf of 80 boxes=

Since probability of cracked is.05 thus in a box of 10, EV of how many cracked in ONE box is .5.

So out of 80 boxes the EV of those cracked is .5 times 80= 40.

Thus those NOT cracked is 80 times 10 minus 40= 800- 40= 760= Expected value for those not cracked.

Part 2: EV of the number of boxes which do NOT contain a cracked egg.

(.95)^10= .5987= probability that a box has NO cracked eggs.

EV value out of 80= .5987 times 80= 47.896

Thanks Slypie. I now understand why I did them wrong before. Thanks for helping.

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