Weel3Assignment1 clean (Compatibility Mode] -Word munira ward Draw Design Layout

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Weel3Assignment1 clean (Compatibility Mode] -Word munira ward Draw Design Layout References Mailings ReviewView Tell me what you want to do Times New R-.112 Aa Blu-x,x' A···:: tE. a- 11 Nrmall 1 No Spac- Heading! Heading 2 Title Sttitle Suttle En. Emphasis · Intense E- String Paragraph ayles 3. p.133,#8 IQ some tests are standardized to a normal model with a mean of 100 and standard deviation of Some IQ tests are standardized to a normal model, with a mean of 100 and a standard deviation of 16 16 O a) In what interval would you expect the central 95% of iq scores to be found? b) About what percent of people should have iq scores above 116? c) About what percent of people should have iq scores between 68 and 84? d) About what percent of people should have iq scores above 132? e) Why can't we use the 68-95-99.7 Rule to find the percentage of people that should have IQs above 108? search

Explanation / Answer

= 100 = 16

X = + Z

a) From Z table for 2.5% and 97.5%,

Z = -1.96 and 1.96

X = 100 - 1.96*16 and X = 100 + 1.96*16

= 68.64, 131.36.

b) 116 = 100 + 16Z

=> Z = 1

From tables, probability is 0.8413

Percentage of people above 116 = 1 - 0.8413 = 0.1587

c) 68 = 100 + 16Z

=> 16Z = -32

=> Z = -2

P(Z) = 0.228

84 = 100 + 16Z

=> 16Z = -16

=> Z = -1

P(Z) = 0.1587

Percentage between the values = (0.228 - 0.1587) * 100 = 6.93%

d) 132 = 100 + 16Z

=> 16Z = 32

=> Z = 2

P(Z) = 0.9772

Percetnage greater than 132 = (1 - 0.9772) * 100 = 2.28%

e) 108 = 100 + 16Z

=> -8 = 16Z

Z = -1/2

If 68-95-99.7 rule was to be applied, Z sholud have been 2, 4 or 6.

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