PSYCH 311 WSU Standard Normal Distribution Questions

PSYCH 311 WSU Standard Normal Distribution Questions

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U1.5 DA Answer the following questions and upload your work into Canvas. Be sure to write your name on your answer sheet, number your answers, show your work, organize your work in a logical and readable order, and upload a single submission (if you have multiple pages of work, take pictures of your work and copy/paste/drop into a single document). Use VassarStats, with the accompanying recorded demo, to answer the questions below. Find p from z: 1. Find p > z = 1.28 2. Find p < z = –.37 3. Find p between z = ±.93 Find X from p: For questions 4 and 5, use the following population parameters to find p from X: μ = 28.29, σ = 3.87. 4. What is the raw score (X) that corresponds to p = .309 in the lower tail of the distribution? 5. What are the raw scores (X’s) that corresponds to p = .92 in the two tails of the distribution combined? Find z from p: For questions 6 and 7, use the mean and standard deviation of a normal z-distribution to find p from z. 6. What is the z-score that corresponds to p = .115 in the upper tail of the distribution? 7. What are the z-scores that corresponds to p = .050 in the two tails of the distribution combined? U1.5 HW Answer the following questions and upload your work into Canvas. Be sure to write your name on your answer sheet, number your answers, show your work, organize your work in a logical and readable order, and upload a single submission (if you have multiple pages of work, take pictures of your work and copy/paste/drop into a single document). The purpose of this assignment is to get you comfortable with ESTIMATING values. IMPORTANT: To benefit from the estimation practice, do NOT use your calculator! Figure out the answers (or as close as you can estimate) just by drawing (and shading) your distributions. Part A: Estimate z from X. μ = 52, σ = 5, X = 57 1. Draw the distribution described in the problem. Be sure to label the mean and the standard deviation on the xaxis. • Find X in the distribution you drew and mark that spot on the distribution. • Looking at the position of X on the x-axis, estimate z. Part B: Estimate p from z. p (z > –1.00), μ = 200, σ = 20 2. Draw the distribution described in the problem. Be sure to label the mean and the standard deviation on the xaxis. • Draw a vertical line through the distribution at z. • Shade the portion of the distribution being asked for in the problem. Remember that the sign points to the direction of shading relative to z. • With the 50% and 68% rules in mind, estimate p. You may use > or < signs if you’d like (e.g., p .15 but p < .50). Remember that this is an estimate, not an exact number. Part C: Estimate p from X (by way of z). p (X > 86), μ = 88, σ = 4 3. Draw the distribution described in the problem. Be sure to label the mean and the standard deviation on the xaxis. • Find X in the distribution you drew and mark that spot on the distribution. • Draw a vertical line through the distribution at X. • Shade the portion of the distribution being asked for in the problem. Remember that the sign points to the direction of shading relative to X. • With the 50% and 68% rules in mind, estimate p. You may use > or < signs if you’d like (e.g., p .15 but p < .50). Remember that this is an estimate, not an exact number. Part D: Estimate z from p. What z-score corresponds to the highest 25% of the z-distribution? 4. Draw the distribution described in the problem. Be sure to label the mean and the standard deviation on the xaxis. • Draw a vertical line (or lines) through the distribution using p. • Shade the portion of the distribution being asked for in the problem. Note that when you aren’t provided a > or < sign, you must interpret what higher/highest/better/above and lower/lowest/below means. • With the 50% and 68% rules in mind, estimate z. You may use ≈ sign if you’d like (e.g., z ≈ 1.30 or z is between 1.0 and 2.0). Remember that this is an estimate, not an exact number. Part E: Estimate X from z. A score (X) has a z = 1.50 in a distribution in which μ = 120, σ = 8. What is X? 5. Draw the distribution described in the problem. Be sure to label the mean and the standard deviation on the xaxis. • Find z in the distribution you drew and mark that spot on the distribution. • Looking at the position of z on the x-axis, estimate X. Part F: Estimate X from p (by way of z). The distribution of Psych 311 final point total is normal with μ = 158, σ = 10. If you must have a minimum of C– (70%) or better to certify into the Psych major, what is the minimum number of points needed to “pass?” 6. Draw the distribution described in the problem. Be sure to label the mean and the standard deviation on the xaxis. • Draw a vertical line through the distribution at X. • Shade the portion of the distribution being asked for in the problem. Note that when you aren’t provided a > or < sign, you must interpret what higher/highest/better/above and lower/lowest/below means. • With the 50% and 68% rules in mind, estimate X. You may use > or < signs if you’d like (e.g., X < 50 or X > 80 but X < 50). Remember that this is an estimate, not an exact number.
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