Week 7, Lab 8
For this deliverable, you should draw a curve by hand.
Look at this lab’s videos to understand how to carry out the exercises.
Due before next class, on Wednesday 10/14
This deliverable comes from the Open Intro Statitstics Book, p. 142
Respond to the questions by answering to the post.
1. What percent of a standard normal distribution N (μ = 0, σ = 1) is
found in each region? Hint! Be sure to draw a graph and use the distribution tables on the Resources page.
(a) Z score −1.35
(b) Z score above 1.48
(c) Between Z score of −0.4 and Z score of 1.5
(d) Z score below – 2 and Z score above 2
2. Sophia who took the Graduate Record Examination (GRE) scored 160 on the Verbal Reasoning section and 157 on the Quantitative Reasoning section. The mean score for the Verbal Reasoning
section for all test takers was 151 with a standard deviation of 7, and the mean score for the Quantitative Reasoning was 153 with a standard deviation of 7.67. Suppose that both distributions are nearly normal.
(a) Write down the short-hand for these two normal distributions.
(b) What is Sophia’s Z-score on the Verbal Reasoning section? On the Quantitative Reasoning section?
Draw a standard normal distribution curve and mark these two Z-scores.
(c) What do these Z-scores tell you?
(d) Relative to others, which section did she do better on?
(e) Find her percentile scores for the two exams.
(f) What percent of the test takers did better than her on the Verbal Reasoning section? On the Quantitative
Reasoning section?
(g) Explain why simply comparing raw scores from the two sections could lead to an incorrect conclusion
as to which section a student did better on.
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1.
A. 8.85%
B. 6.94% = 7%
C. 59%
D. 2.28%
2.
A. Verbal Reasoning= N ( μ= 151,σ = 7)
Quant. Reasoning= N (μ= 153,σ= 7.67)
B. Verbal Reasoning = 1.29 Quant. Reasoning = 0.52
C. The Z-score tells us how far away from the mean Sophia score is
D. Based on the chart Sophia did better on the Verbal Reasoning section (1.29)
E. Verbal Reasoning Percentile ( 90.15%) Quant. Reasoning Percentile ( 69.8%)
F. 30.15% did better than her on the Verbal and 9.85% did better than her on the Quant.
G. Comparing raw scores for the two sections would give us incorrect answers because it would not give us the exact position on the Z-score or even if you do the mean, median and mode
1a. 8.85%
1b. 7%
1c. 59%
1d. 2.28%
2a. V– N(μ=151, σ=7) Q– N(μ=153, σ=7.67)
2b. Z-score for verbal= 1.29 and z-score for quantitative is 0.52.
2c. These z-scores tell me how far each value is from the mean, so she scored 1.29 standard deviations above the mean on the verbal reasoning section and 0.52 standard deviations above the mean on the quantitative reasoning section.
2d. Verbal reasoning section
2e. V= 90%, Q= 70%
2f. 10% did better than her on the verbal section and 30% did better than her on the quantitative section.
2g. We cannot compare the raw scores since they are on different scales, comparing her percentile scores is more appropriate when comparing her performance to others.
1
A) 8.85%
B) 6.94%
C) 58.86%
D) 2.28
2
A) Verbal Reasoning N (μ=151, σ=7)
Quantitive reasoning N (μ=153, σ=7.67)
B) Verbal Reasoning Z score is 1.29
Quantitive reasoning Z score is 0.52
C) The Z score tells the distance that the score is from the mean.
D) She did better on verbal reasoning.
E) Verbal reasoning: 90.15 percentile
Quantitive reasoning: 69.85 percentile
F) On the verbal reasoning section 10.03% did better and on the quantitative reasoning section 30.15% did better.
G) Comparing the raw scores could lead to an incorrect conclusion because they may not be comparable before being standardized.
1a- 8.85%. 1B- 6.94%. 1C- 58.86%. 1D- 2.28%
2A- Verbal reasoning:N (μ= 153, σ= 7.67) and the quantitive is (μ= 153, σ= 7)
2B-The verbal reasoning score is 1.28 and the quantitive is 0.52
2C- The Z score will tell us the mean.
2D- she ended up doing better on the verbal.
2E. The percentiles are 89.97% and 69.85%
2F. the verbal is 10.03% did better then her and for the quantitive 30.15% did better.
2G. raw scores won’t give you correct numbers because all 3 (median, mode, mean) are different
1a) 8.85%
1b) 6.94%
1c) 58.86%
1d) 2.28%
2a) Quantitative Reasoning N (μ= 153, σ= 7.67)
Verbal Reasoning N (μ= 151, μ= 7)
2b) Quantitative Reasoning Z-score = 0.52
Verbal Reasoning Z-score = 1.28
2c) The z-scores lets us know how far from the mean their actual scores are.
2d) She did better on the verbal reasoning.
2e) Quantitative Reasoning 69.85%
Verbal Reasoning 89.97%
2f) Quantitative Reasoning 30.15% did better
Verbal Reasoning 10.03% did better.
2g) Comparing raw scores from different sections could lead to incorrect conclusions because both scores have different averages, standard deviations, medians and modes.
1-a) 8.85%
b) 6,94%
d) 2.28%
2) Verbal Reasoning N(Mean =153, std = Quantitative Reasoning (N(Mean =153, stigma =7.67
Verbal reasoning Z score =1,28
Quantitative Reasoning =0.52
d)Verbal reasoning performance was higher
e)Percentiles 89.97% and 69.85%
f)10.035 percent for verbal reasoning and 30.155 for quantitative
g)Comparing raw scores will not give an accurate position of the scores.
1.
A. 68%
B. 6.94%
C. 58.86%
D. 2.28%
2.
A. Verbal reasoning: N (μ=151, σ=7). Quantitative reasoning: N (μ=153, σ=7.67).
B. Verbal reasoning z score is 1.28, quantitative reasoning z-score is 0.52
C. Sophia’s z score is far from the mean.
D. Verbal reasoning because it is a higher positive z-score, 1.28
E. Percentile for verbal: 89.7%, for quantitative: 69.85%
F. Verbal reasoning, 10.03% did better, in quantitative, 30.15% did better.
G. Comparison of raw scores does not give exact position. Both sections have different averages, means, modes, medians and standard deviation.
1(a). 8.85% (b). 6.94% (c). 58.86% (d). 2.28% 2(a). The verbal reasoning fir this GRE isN ( μ=151, σ=7) The quantitative reasoning for this GRE is N (μ=153, σ= 7.67)
(b). For verbal reasoning, the Z- score is 1.28. For Quantitative reasoning, the Z-score is 0.52.
(c). The Z-scores listed lets us know the differences of the mean of Sophia`s scores.
(d). The data given, mostly the highest Z score lets us know that Sophia scored better on verbal reasoning.
(e).Quantitative Reasoning: 69.85%. Verbal Reasoning: 89.97%.
(f). Quantitative reasoning section, 30.15% performed better. The Verbal reasoning section, 10.03% performed better.
(g). Utilizing the resources given and the data I applied; I found out that the median, mode, and mode are different. Therefore, when comparing the raw scores the number of students scores are not accurate.
1) 68%
a) 8.85%
b) 93.06%
c) 0.5886 -> 58.86%
d) 1
2)
a) N (μ=151, σ=7) N (μ=153, σ=7.67)
b) Z= 160-151/7 Z = 1.29 for verbal reasoning Z= 157-153/7.67 Z= 0.52 quantitative
c) it tells us the mean
d) this shows that sophia scored higher on the verbal reasoning
e) verbal 0.9015 –> 90 percentile and quantitative 0.6985 –> 70 percentile
f) comparing raw scores can cause incorrect comparison because both have different average score and standard deviation. one have to even the scale in order to get right comparison
1)
a. 8.85%
b. 6.94%
c. 58.86%
d. 2.28%
2)
a. The verbal reasoning is N (μ=151, σ=7). The quantitative reasoning is N (μ=153, σ=7.67).
b. Sophia’s Z-score on the verbal reasoning is Z-score of 1.28. Sophia’s Z-score on the quantitative reasoning is Z-score of 0.52.
c. These Z-scores tells me that Sophia’s scores is faraway in the mean.
d. Sophia did better on the verbal reasoning because it shows how their is a high positive Z-score of 1.28.
e. Her percentile score for verbal reasoning is 89.97% and for quantitative reasoning is 69.85%.
f. On the verbal reasoning section 10.03% did better than her and on the quantitative reasoning section 30.15% did better than her.
g. From comparing raw scores they do not give the correct number of the students scores in statistics because the mean, median, and mode are unlike in both sections.
1. (a) 8.85%
(b) 6.94%
(c) 58.86%
(d) 2.28%
2. (a) Verbal Reasoning: N (μ=151, σ=7). Quantitative Reasoning: N (μ=153, σ=7.67).
(b) Verbal reasoning: Z-score of 1.28. Quantitative reasoning: Z-score of 0.52.
(c) These Z-scores tell us how far from the mean Sophia’s scores lie.
(d) In verbal reasoning because it has the highest positive Z score (1.28).
(e) Verbal: 89.97% Quantitative: 69.85%
(f) On verbal section, 10.03% did better. On quantitative section, 30.15% did better.
(g) Simply comparing raw scores do not give the exact position of student’s score on the data in comparison to the average scores which are different in two sections.