Question

Finding probabilities for the Normal (bell-shaped) distribution

Name three different ways you can find probabilities for the Normal distribution.

Answer 1

Answer:

Name three different ways you can find probabilities for the Normal distribution:

Three different ways to find the probabilities for the normal distribution are:

1) Using the statistical tables, as the cumulative probabilities of the standard normal distribution are listed there and as a result probabilities of the normal distribution with any parameter values can be found out by converting it in the standard form.

2) Using the Excel software, functions which are useful are NORMSDIST and NORMSINV.

3) Empirical rule can be used to obtain the same which is also known as 68.3-95-99.7 rule.

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Answer 2

1. Z-table: One of the common methods to find probabilities for the Normal distribution is by using a Z-table (also known as the standard normal table). The Z-table provides the cumulative probability for a standard normal distribution (mean = 0, standard deviation = 1). To find the probability for a specific value (x) in a normal distribution with a given mean (μ) and standard deviation (σ), you first standardize the value using the formula: Z = (x - μ) / σ. Then, you look up the corresponding cumulative probability in the Z-table.

2. Cumulative Distribution Function (CDF): The Cumulative Distribution Function (CDF) of a normal distribution gives the probability that a random variable is less than or equal to a specific value. For a given value (x) in a normal distribution with mean (μ) and standard deviation (σ), you can use the CDF formula to find the probability: P(X ≤ x) = Φ((x - μ) / σ), where Φ is the standard normal CDF.

3. Statistical Software: Using statistical software, such as R, Python with libraries like scipy, or statistical calculators, you can directly input the mean, standard deviation, and the specific value of interest to get the probability for the Normal distribution. These tools have built-in functions to calculate probabilities based on the Normal distribution, making it convenient and efficient for various scenarios.