1. Data are drawn from a bell-shaped distribution with a mean of 160 and a stand
ID: 3072286 • Letter: 1
Question
1. Data are drawn from a bell-shaped distribution with a mean of 160 and a standard deviation of 5. There are 1,400 observations in the data set.
a. Approximately what percentage of the observations are less than 170? (Round your answer to 1 decimal place.)
percentage of observations ______________%
b. Approximately how many observations are less than 170? (Round your answer to the nearest whole number.)
number of observations ______________
2. Data with 850 observations are drawn from a bell-shaped distribution with a mean of 72 and a standard deviation of 17. Approximately how many observations are more than 106? (Round your answer to the nearest whole number.)
Number of observations_______________
Explanation / Answer
According to empirical rule,
i) Approximately 68% of the data fall within 1 standard deviations of thr mean.
ii) Approximately 95% of the data fall within 2 standard deviations of the mean.
iii) Approximately 99.7% of the data fall within 3 standard deviations of the mean.
Q.1) Given that, mean = 160
standard deviation = 5
Total observations = 1400
mean + 2 S.D. = 160 + (2 * 5) = 170
From empirical rule ii),
a) approximately, 2.5% + 95% = 97.5 % of the observations are less than 170.
b) expected observation that are less than 170 are,
1400 * 0.975 = 1365
Therefore, approximately 1365 observations are less than 170.
Q.2) Given that, mean = 72
standard deviation = 17
Total observations = 850
Mean + 2S.D.= 72 + (2 * 17) = 106
According to empirical rule ii), approximately 2.5% of the observations are more than 106
Expected observations that are more than 106 are,
850 * 0.025 = 21.25 ( approx 21)
Therefore, approximately 21 observations are more than 106
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