11/15/2023 0 Comments Stat crunch find corresponding zscoreSketch this distribution and find the area to the right (probability above) for each score. Test scores of four students selected at random are 1920, 1240, 2350, and 1390. In a recent year, the mean ( ) test score was 1498 and the standard deviation ( ) was 316. The test scores are normally distributed. Consider the last example concerning the SAT: Ex: The SAT is an exam used by colleges and universities to evaluate undergraduate applicants. In this section you will get the chance to apply the probabilities (areas) from the Standard Normal Distribution to real- life situations. Find z-scores to calculate Area Under the Normal Curve (using StatCrunch or Calculator) Sketch Normal Distribution along with Standard Normal Distribution Section 5.2: Normal Probability Distributions: Finding Probabilities Objectives: Sketch this distribution, find the z-scores for each value, and determine whether any of the values are unusual when compared to the mean and standard deviation. P(-1.5 z 1.25) = _ Ex: The SAT is an exam used by colleges and universities to evaluate undergraduate applicants. **Label the z-score and the area.** StatCrunch: Stat menu, Calculators, Normal, Between, enter z-scores, Compute TI-83/84: 2nd VARS normalcdf( -1.5 Comma 1.25 Comma 0 Comma 1 enter P(z -2.3) = _ Ex: Find the shaded area. **Label the z-score and the area.** StatCrunch: Stat menu, Calculators, Normal, Standard, enter inequality symbol and z-score, Compute TI-83/84: 2nd VARS normalcdf( -2.3 Comma 1000000000 Comma 0 Comma 1 enter **Label the z-score and the area.** a) b) Hint: Use the fact that the total area (probability) is 1. **Label the z-score and the area.** StatCrunch: Stat menu, Calculators, Normal, Standard, enter inequality symbol and z-score, Compute TI-83/84: 2nd VARS normalcdf( -1000000000 Comma -0.24 Comma 0 Comma 1 enter P(z -0.24) = 0.4052Įx: Find the area to right of each z-score. **Label the z-score and the area.** StatCrunch: Stat menu, Calculators, Normal, enter inequality symbol and z-score, Compute TI-83/84: 2nd VARS normalcdf( -1000000000 Comma 1.15 Comma 0 Comma 1 enter P(z 1.15) = 0.8749 Ex: Confirm that the cumulative area that corresponds to z = -0.24 is 0.4052. **Also and for any continuous probability distribution.**Įx: Confirm that the area to the left of z = 1.15 is 0.8749. You do NOT need to learn how to read the Standard Normal Table.** **All probability calculations will be done with either StatCrunch or the TI 83/84 calculator. This means we will use the z-score formula to transform any data value into a “measure of position” with the formula: Note: Every normal distribution can be transformed into the Standard Normal Distribution (the distribution for z- scores). Which normal curve has the greatest mean? Which normal curve has the greatest standard deviation? (Remember that any probability distribution has two properties: all probabilities are between 0 and 1 and the sum of the probabilities is 1.) **Probabilities = Areas under the curve**Įx: Consider the normal distribution curves below. By using the normal distribution curve, we are treating the data as a continuous random variable that has its own continuous probability distribution. Why do we need to study this? Eventually we will use these probabilities and z-scores to make decisions. Now we will use these normal curves to find probabilities (areas) and z-scores for any data value. From Test 1 remember that normal curves have z-scores (for any data value) and areas under the curve (one way: Empirical Rule). In this section we will revisit histograms which can be estimated with normal (symmetric, bell-shaped) curves. Use z-scores to Calculate Area Under the Standard Normal Curve (using StatCrunch or Calculator) Section 5.1: Intro to Normal Distributions and the Standard Normal Distributions Objectives: Chapter 5: Normal Probability Distributions
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