Sorry to disturb, I have 4 questions that i do not understand how to do and would like help from all of you.

[Rubendren]

Q1. A number which consists of four digits is formed from a set of integers {1,2,3,4,5,6,7,8,9}.
Events A,B and C are defined as follows:

A: The number does not contain digit 6.
B: The number consists of four different digits.
C: The number begins with digit 3.

Q2. A fair dice is rolled once. If the score is 3 or more, then the 'outcome' X is the score. if the score is 1 or 2, then the dice has to be rolled once again and the 'outcome'X is the sum of score of the two rolls.
a. Tabulate the probability distributions P (X=x)
b. Hence, calculate the mean and variance of X.

Q3. Past records show that the times, in seconds, taken to run 150m by children at a school can be modelled by a normal distribution with a mean of 10.13 and a standard deviation of 1.30.

a. A child from the school is selected at random. Find the probability that this child runs 150m in less than 13 seconds.
b. On sports day, the school awards certificate to the fastest 25% of the children in the 150m race. Estimate, to 2 decimal places, the slowest time taken to run 100m for which child will be awarded a certificate.

 

[Deleted member 4993]

Q1. A number which consists of four digits is formed from a set of integers {1,2,3,4,5,6,7,8,9}.
Events A,B and C are defined as follows:

A: The number does not contain digit 6.
B: The number consists of four different digits.
C: The number begins with digit 3.

Q2. A fair dice is rolled once. If the score is 3 or more, then the 'outcome' X is the score. if the score is 1 or 2, then the dice has to be rolled once again and the 'outcome'X is the sum of score of the two rolls.
a. Tabulate the probability distributions P (X=x)
b. Hence, calculate the mean and variance of X.

Q3. Past records show that the times, in seconds, taken to run 150m by children at a school can be modelled by a normal distribution with a mean of 10.13 and a standard deviation of 1.30.

a. A child from the school is selected at random. Find the probability that this child runs 150m in less than 13 seconds.
b. On sports day, the school awards certificate to the fastest 25% of the children in the 150m race. Estimate, to 2 decimal places, the slowest time taken to run 100m for which child will be awarded a certificate.

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this assignment.

 

[HallsofIvy]

Q1. A number which consists of four digits is formed from a set of integers {1,2,3,4,5,6,7,8,9}.
Events A,B and C are defined as follows:

Actually there is no question asked here or for any of the others! I presume you are to tell how many different ways each of these can happen.
These all use "the fundamental counting principle": if event A can occur in "n" ways and event B can independently occur in "m" ways then they can occur together in mn ways. If you were given a problem like this, you have probably seen that.

A: The number does not contain digit 6.

The first digit can be any of the other 8 digits. The second digit can also be any of 8 digits. Same for the third and fourth digits. So this is 8(8)(8)(8).

B: The number consists of four different digits.

The first digit can be any of the 9 digits, the second can be any of the remaining 8 digits, the third can be any of the remaining 7, and the fourth any of the remaining 6.

C: The number begins with digit 3.

The first digit must be "3" but we can choose the second, third, and fourth digits how many ways?

Q2. A fair dice is rolled once. If the score is 3 or more, then the 'outcome' X is the score. if the score is 1 or 2, then the dice has to be rolled once again and the 'outcome'X is the sum of score of the two rolls.

My standard rant: "dice" is the plural of the singular "die". You roll a fair "die" not "a dice"!
By "outcome" you mean the number showing on the die?

a. Tabulate the probability distributions P (X=x)
A single die has 6 possible outcomes: 1, 2, 3, 4, 5, 6, each equally likely. That is, each probability is the same and, as always, those probabilities add to 1. What number, added to itself 6 times, adds to 1? Of course, "adding a number to itself 6 times" is the same as "multiplying the number by 6". What number, multiplied by 6, equals 1?

b. Hence, calculate the mean and variance of X.

What are the definitions of "mean" and "variance"?

Q3. Past records show that the times, in seconds, taken to run 150m by children at a school can be modelled by a normal distribution with a mean of 10.13 and a standard deviation of 1.30.

a. A child from the school is selected at random. Find the probability that this child runs 150m in less than 13 seconds.
b. On sports day, the school awards certificate to the fastest 25% of the children in the 150m race. Estimate, to 2 decimal places, the slowest time taken to run 100m for which child will be awarded a certificate.

What do you know about the "normal distribution" Typically you have to use a table or program to get normal distribution values. Do you have either of those available? There is a table at https://en.wikipedia.org/wiki/Standard_normal_table or a program here: https://mathcracker.com/normal_probability.[/quote][/QUOTE]