Follow these steps: Draw a picture of the normal distribution. Translate the problem into one of the following: p(X < a), p(X > b), or p(a < X < b). Shade in the area on your picture. Standardize a (and/or b) to a z-score using the z-formula: Look up the z-score on the Z-table (see below) and find its corresponding probability. a. Find the row of the table corresponding to the leading digit (ones digit) and first digit after the decimal point (the tenths digit). b. Find the column corresponding to the second digit after the decimal point (the hundredths digit). c. Intersect the row and column from Steps (a) and (b). If you need a "less-than" probability — that is, p(X < a) — you're done. If you want a "greater-than" probability — that is, p(X > b) — take one minus the result from Step 4. If you need a "between-two-values" probability — that is, p(a < X < b) — do Steps 1–4 for b (the larger of the two values) and again for a (the smaller of the two values), and subtract the results. The probability that X is equal to any single value is 0 for any continuous random variable (like the normal). That's because continuous random variables consider probability as being area under the curve, and there's no area under a curve at one single point. This isn't true of discrete random variables. Suppose, for example, that you enter a fishing contest. The contest takes place in a pond where the fish lengths have a normal distribution with mean μ = 16 and standard deviation σ = 4
The distribution of fish lengths in a pond This figure shows a picture of X's distribution for fish lengths. You can see where the numbers of interest (8, 16, and 24) fall.Next, translate each problem into probability notation. Problem 1 is really asking you to find p(X < 8). For Problem 2, you want p(X > 24). And Problem 3 is looking for p(16 < X < 24). Step 3 says change the x-values to z-values using the z-formula: For Problem 1 of the fish example, you have the following: Similarly for Problem 2, p(X > 24) becomes And Problem 3 translates from p(16 < X < 24) to The following figure shows a comparison of the X-distribution and Z-distribution for the values x = 8, 16, and 24, which standardize to z = –2, 0, and +2, respectively. Standardizing numbers from a normal distribution (X) to numbers on the Z-distribution Now that you have changed x-values to z-values, you move to Step 4 and calculate probabilities for those z-values using the Z-table.In Problem 1 of the fish example, you want p(Z < –2); go to the Z-table and look at the row for –2.0 and the column for 0.00, intersect them, and you find 0.0228 — according to Step 6, you're done. The probability of a fish being less than 8 inches is equal to 0.0228. For Problem 2, find p(Z > 2.00). Because it's a "greater-than" problem, this calls for Step 7. To be able to use the Z-table, you need to rewrite this in terms of a "less-than" statement. Because the entire probability for the Z-distribution equals 1, you know p(Z > 2.00) = 1 – p(Z < 2.00) = 1 – 0.9772 = 0.0228 (using the Z-table). So, the probability that a fish is greater than 24 inches is also 0.0228. (Note: The answers to Problems 1 and 2 are the same because the Z-distribution is symmetric; refer to the first figure.) In Problem 3, you find p(0 < Z < 2.00); this requires Step 8. First find p(Z < 2.00), which is 0.9772 from the Z-table. Then find p(Z < 0), which is 0.5000 from the Z-table. Subtract them to get 0.9772 – 0.5000 = 0.4772. The probability of a fish being between 16 and 24 inches is 0.4772. The Z-table does not list every possible value of Z; it just carries them out to two digits after the decimal point. Use the one closest to the one you need. And just like in an airplane where the closest exit may be behind you, the closest z-value may be the one that is lower than the one you need. About This ArticleThis article is from the book:
About the book author:Deborah J. Rumsey, PhD, is an Auxiliary Professor and Statistics Education Specialist at The Ohio State University. She is the author of Statistics For Dummies, Statistics II For Dummies, Statistics Workbook For Dummies, and Probability For Dummies. This article can be found in the category:
How do you find the probability with percentages?You calculate probability by dividing the number of successes by the total number of attempts. Your result will be a number between 0 and 1, which can also be expressed as a percent if you multiply the number by 100%.
What is the formula for probability in statistics?Where, P(A) is the probability of an event “A” n(A) is the number of favourable outcomes. n(S) is the total number of events in the sample space.
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Basic Probability Formulas.. What does a probability of 10% mean?A probability of 0.1 means there is a 1 in 10 chance of an event happening, or a 10% chance that an event will happen. Weather forecasters might tell us that there is a 70% chance of rain.
How do you find the probability of two percentages?Just multiply the probability of the first event by the second. For example, if the probability of event A is 2/9 and the probability of event B is 3/9 then the probability of both events happening at the same time is (2/9)*(3/9) = 6/81 = 2/27.
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