Scores on a math final are normally distributed with a mean of 72 and a standard deviation of 3.2.a) Leisha scored 80 on the exam. Find the z score that corresponds with this grade. Round to the nearest tenth.b) What was Leisha’s percentile on the test? That is, what percentage of students scored lower than her? Z*scorePercentileZ*scorePercentileZ*scorePercentileZ*scorePercentile−2.11.79−0.5030.850.5069.152.198.21−2.02.28−0.4532.640.5570.882.298.61−1.92.87−0.4034.460.6072.572.398.93−1.83.59−0.3536.320.6574.222.499.18−1.74.46−0.3038.210.7075.802.599.38−1.65.48−0.2540.130.7577.342.699.53−1.56.68−0.2042.070.8078.812.799.65−1.48.08−0.1544.040.8580.232.899.74−1.39.68−0.1046.020.9081.592.999.81−1.211.51−0.0548.010.9582.893.099.87−1.113.57−0.050.001.084.133.599.98

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Answered: Scores on a math final are normally…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Scores on a math final are normally distributed with a mean of 72 and a standard deviation of 3.2.

a) Leisha scored 80 on the exam. Find the z score that corresponds with this grade. Round to the nearest tenth.

b) What was Leisha’s percentile on the test? That is, what percentage of students scored lower than her?

Z*score	Percentile	Z*score	Percentile	Z*score	Percentile	Z*score	Percentile
−2.1	1.79	−0.50	30.85	0.50	69.15	2.1	98.21
−2.0	2.28	−0.45	32.64	0.55	70.88	2.2	98.61
−1.9	2.87	−0.40	34.46	0.60	72.57	2.3	98.93
−1.8	3.59	−0.35	36.32	0.65	74.22	2.4	99.18
−1.7	4.46	−0.30	38.21	0.70	75.80	2.5	99.38
−1.6	5.48	−0.25	40.13	0.75	77.34	2.6	99.53
−1.5	6.68	−0.20	42.07	0.80	78.81	2.7	99.65
−1.4	8.08	−0.15	44.04	0.85	80.23	2.8	99.74
−1.3	9.68	−0.10	46.02	0.90	81.59	2.9	99.81
−1.2	11.51	−0.05	48.01	0.95	82.89	3.0	99.87
−1.1	13.57	−0.0	50.00	1.0	84.13	3.5	99.98

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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