Regardless of the previous results of the dice rolls, the probability of each individual dice roll remains the same. Each time the dice is rolled, there is a 1/6 chance that it will land on a specific number. Therefore, there is a 1/6 chance that the dice will roll a 6 on the sixth roll. 

According to the Law of Large Numbers, the probability of the coin landing on tails after being rolled an infinite number of times is equal to the probability of the coin landing on tails in an individual roll: 50%. 

Time is the independent variable as time is not affected by the other variables but the other variables all change as time lapses.

A continuous variable may assume an infinite number of different values between two given points while a discrete variable may only assume a specific number of specific values between two given points. Given this information, it becomes apparent that the concentration of DNA in a liquid sample and the weight of footballs are both continuous variables.

The Independent variable is what the experimenters are directly manipulating-- here, that is the strength of the Chemical XYZ.

The Dependent variable is the variable that changes based on the Independent variable-- in this case, it is the amount of oil on participants' scalps. 

A Dependent variable is what changes based on the independent, manipulated variable.

The Independent variables are the Room Temperature and the Lighting state, which the researchers were manipulating themselves.

The Dependent variable is the Mouse Food Intake, which is the variable that changed based on how the independent variables changed.

Remember how the mean and standard deviation of a random variable are affected when it is multiplied by a constant.

Any linear combination of independent random variables is also normally distributed with the mean and variance depending on the weights on the random variables. The mean is additive in the sense that

Each  is , so the sum is equal to zero.

This means the sum of the average 

 is .

The variance satisfies

 because of independence.

This means that the average is normally distributed with mean  and variance .

There is a relatively simple way of doing this problem. The sum of any set of independent normal random variables is also distributed normally. So  has a normal distribution. Now we can compute the mean and variance. The mean is additive:

Variance is also additive in some sense, when the random variables are independent:

Thus,  is normally distributed with mean  and variance .

This sum is a standard normal distribution.

The chance that  is thus , if we use a normal table.

To find the mean you sum up all of your values then divide by the total amount of values.  The total sum of the weights is  and there are 10 melons.