Download Week-III

Week-IV
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14-Sample variance and
standard deviation
1-Sample variance
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2-Review and intuition why we divide by
n-1 for the unbiased sample variance
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3-Sample standard deviation and bias
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2-MODELING DISTRIBUTIONS OF DATA
1-Describing location in a distribution
• Normal distribution problems and z-score
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Normal Distribution
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https://www.wolframalpha.com/input/?i=int+1%2Fsqrt(2*pi)*e%5E(x%5E2%2F2)+from+0+to+.53
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z-score
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The grades on a statistics mid-term for a high school are normally distributed with
µ=81 and σ=6.3.
Calculate the z-scores for each of the following exam grades. Draw and label a
sketch for each example.
A) 65
B) 83
C) 93
D) 100
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Assume that the mean weight of 1 year-old girls in the US is normally
distributed with a mean of about 9.5 kilograms with a standart deviation of
approximately 1.1 kilograms.
Without using a calculator, estimate the percentage of 1 year-old girls in the
US that meet the following conditions.
Draw a sketch and shade the proper region for each problem.
(a) Less than 8.4 kg
(b) Between 7.3 kg and 11.7 kg
(c) More than 12.8 kg
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For a standart normal distribution, place the following in order from smallest
to largest.
(a)
(b)
(c)
(d)
(e)
The percentage of data below 1
The percentage of data below -1
The mean
The standart deviation
The percentage of data above 2
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4- More empirical rule
and z-score practice
The 2007 AP Statistics examination scores were not normally distributed, with
µ=2.80 and σ=1.34. What is the approximate z-score that corresponds to an
exam score of 5 (The scores range from 1-5).
(a)
(b)
(c)
(d)
(e)
0.786
1.46
1.64
2.20
A z-score can not be calculated because the distribution is not normal.
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The heights of 5th grade boys in the United States is approximately noramally
distributed with a mean height of 143.5 cm and a standart deviation of about
7.1 cm. What is the probability that a randomly chosen 5th grade boy would
be taller than 157.7 cm?
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