LastName FirstName 99.7% of data are within 3 standard deviations of the mean (-
ID: 3060176 • Letter: L
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LastName FirstName 99.7% of data are within 3 standard deviations of the mean (-3 to + 3e) 95%, within 2 standard deviations 68% within- I standard deviatiorn 34% 34% 0.15% 2.35% 2.35%, 0.15% 13,5% 13.5% I. In the questions you will find it extremely helpful to drawe and label a rough sketch of a bell- curves distribution for the given sample statistics or population parameters. (4 points each) a. The scores from a state standardized test have a bell-shaped distribution with a mean of -100 and a standard deviation . 15. Use the Empirical Rule to predict the approximate percentage of students with scores between 70 and 130. A) 95% B) 68% C) 99.7% D) 100% The scores from a state standardized test have a mean -80 and a standard deviation of 10, The distribution of the scores is roughly bell shaped. Use the Empirical Rule to predict the approximate percentage of scores that lie between 60 and 80. b. B)68% C) 34% D)95% A) 47.5% The average score of local students on a college entrance exam with -110, with a standard deviation c. of 5. The distribution is roughly bell shaped. Use the Empirical Rule to predict the approximate the percentage of local students with scores above 120 ie, 20. B) 5% C)95% D)97.5% A) 2.5% d. A study was designed to investigate the effects of two variables (1) a student's level of biostatistics anxiety and 2) teaching method - on a student's achievement in a biostatistics course. Students had a low level of biostatistics anxiety were taught using the traditional expository method. These studen ts obtained a sample mean score of 460 with a standard deviation of 50 on a standardized test. Assuming a bell-shaped distribution, what percentage of scores e A) approximately 97.5% C) approximately 25% B) approximately 95% D) approximately 84%Explanation / Answer
a)
Mean = 100
SD = 15
M-2*SD = 100-30 = 70
M+2*SD = 100+30 = 130
Between M-2*SD and M+2*SD we have 95% of the observations
That will be option - (A)
b)
Mean = 80
SD = 10
M-2*SD = 80-20 = 60
M+2*SD = 80+20 = 100
Between M-2*SD and M+2*SD we have 95% of the observations
Between M-2*SD and M, we have 95/2 = 47.5% of the observations
That will be option - (A)
c)
M = 110
SD = 5
M+2*SD = 110 + 2*5 = 120
Between M-2*SD and M+2*SD we have 95% of the observations
Above M+2*SD we have 2.5% of the observations
That will be Option- (A)
d)
Mean = 460
SD = 50
M-2*SD = 460-50*2 = 360
Above M-2*SD, we have 50+50-2.5 = 97.5% of the scores
That will be Option- (A)
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