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1 Nov 2021
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The probability rule of sum gives the situations in which the probability of a union of events can be calculated by summing probabilities together. It is often used on mutually exclusive events, meaning events that cannot both happen at the same time.
The sum of the probabilities in a probability distribution is always 1.
Step-by-step explanation
Step 1.
By the Central Limit Theorem, we can assume that the sampling distribution of the mean will be normal in most cases. This means that we can take advantage of statistical techniques that assume a normal distribution, as we will see in the next section.
The Central Limit Theorem for Sums: The central limit theorem tells us that for a population with any distribution, the distribution of the sums for the sample means approaches a normal distribution as the sample size increases. In other words, if the sample size is large enough, the distribution of the sums can be approximated by a normal distribution even if the original population is not normally distributed. Additionally, if the original population has a mean of μX and a standard deviation of σx, the mean of the sums is nμx and the standard deviation is ( n) (σx) where n is the sample size.
For example, a set of real numbers, is a continuous or normal distribution, as it gives all the possible outcomes of real numbers. Similarly, a set of complex numbers, a set of prime numbers, a set of whole numbers, etc. are examples of Normal Probability distribution. Also, in real-life scenarios, the temperature of the day is an example of continuous probability.
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Introductory Statistics
OER Edition, 2013
Openstax
ISBN: 9781938168208
Solutions
Chapter
Section
- Problem 1
- Problem 2a
- Problem 2b
- Problem 3a
- Problem 3b
- Problem 4a
- Problem 4b
- Problem 5
- Problem 6a
- Problem 6b
- Problem 7
- Problem 8
- Problem 10
- Problem 10
- Problem 11
- Problem 12
- Problem 13
- Problem 14
- Problem 15
- Problem 16
- Problem 17
- Problem 18
- Problem 19
- Problem 20
- Problem 21
- Problem 22
- Problem 23
- Problem 24
- Problem 25
- Problem 26
- Problem 27
- Problem 28
- Problem 29
- Problem 30
- Problem 31
- Problem 32
- Problem 33
- Problem 34
- Problem 35
- Problem 36
- Problem 37a
- Problem 37b
- Problem 37c
- Problem 38
- Problem 39
- Problem 40
- Problem 41
- Problem 42
- Problem 43a
- Problem 43b
- Problem 44
- Problem 45
- Problem 46
- Problem 47a
- Problem 47b
- Problem 48
- Problem 49
- Problem 50
- Problem 51
- Problem 52
- Problem 53
- Problem 54
- Problem 55
- Problem 56
- Problem 57
- Problem 58
- Problem 59
- Problem 60