PSYCH 301 – 1st Edition Lecture 5Random SamplingOutline of Last Lecture I. Normal DistributionII. Z ScoresIII. QuestionsOutline of Current Lecture IV. Random SamplingV. Z Scores& ProbabilitiesVI. One-Tailed / Two-Tailed ProbabilitiesVII. Z tableVIII. QuestionsCurrent Lecture – I. Random Samplinga. The area under the bell-curve reflects probabilityb. All probabilities sum to 1These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.c. The z score that is most probable / has the highest probability is the highest point of the curved. The probability of drawing a score above the mean is 50%e. The probability of drawing a score below the mean is also 50%f. The normal distribution has a well-defined shapei.ii. Probability of drawing a score greater than μ+σ = 16%1. ( x >μ+σ ) : 14% + 2% = 16%iii. Probability of drawing a score: μ < x <μ+ 2σ1. 34% + 14% = 48%iv. Probability of drawing a z score: -1 < z < 01. 34% II. Z Scores & Probabilitiesa. Probability of randomly selecting someone with an IQ greater than 70 and less than 115.Z = ( x – μ ) / σ Mean = 100SD = 15Z = (70-100)/15 Z = (115-100) / 15Z= -2 Z=1-2 < Z(IQ) < -1 →.14-1 < Z(IQ) < 0 → +.340 < Z(IQ) < 1 → + .34= .82III. One-Tailed / Two-Tailed Probabilities (2 ways of calculating z scores)a. Non-Directional hypothesis (not picking sides)i. “What is the probability of randomly drawing a z score more extreme (i.e. further away from the mean) than 2?”1. 4%ii. Two-tailed: entertaining both tails of distribution at the same time. (add the negative and positive probability regions together)b. Directional hypothesisi. “What is the probability of randomly drawing a z score larger than 2?”1. 2%ii. One-tailed: either the negative tail OR positive tail ONLYc.i. Two-tailed: z > 2 and z < -2 (add both)ii. One-tailed: z > 2 OR z < -2 (just one)IV. Z tablea. To find z values other than z = -3, -2, -1, 0, 1, 2, or 3, you have to look it upin a z table.b. Z tables list the probability of drawing a particular z scorec. There are 2 different layouts:i. Some tables list the probability of drawing a z score below a certain value (1-p)1.ii. Other tables list the probability of drawing a z score between 0 and a certain value, so they list these values as (0.5-p)1.d. Standard Normal (Z) Table (values correspond to 1 – p)i.ii. The values shown on the table correspond to (1 – p)iii. If you need to find p, you need to find the corresponding number to the z value given and plug it into (p – 1) to get p.Z = 0.44p-1 = 0.67P = 33V. Questionsa. What is the most probable z score, and how many SDs away from the mean is it?i. Most probable is 0 and it is 0 SDs away from the meanb. Do one-tailed or two-tailed tests ask id scores are more extreme than your given z score?i. Two-tailedc. What z score corresponds to p = .05 for two-tailed tests?i. 1 – p(.05) = .95 → look at z table for the closest number to .951. It is between 1.64 and