question archive Students taking an introductory statistics class reported spending an average of 245 dollars on textbooks that semester with a standard deviation of 60 dollars
Students taking an introductory statistics class reported spending an average of 245 dollars on textbooks that semester with a standard deviation of 60 dollars
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Students taking an introductory statistics class reported spending an average of 245 dollars on textbooks that semester with a standard deviation of 60 dollars.
a. 68 percent of students between _______ and _______
b. 95 percent of students between _______ and _______
c. 99.7 percent of students between ______ and _______
d. Approximately what percentage of students spent between $165 and $290 on textbooks that semester?
e. One student spent $260 on textbooks. What percentage of the students spent less than she did on textbooks that semester?
f. 15% of students spend less than ______ on textbooks.
g. 40% of students spend more than _____ on textbooks.
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a)(185,305)
b)(125,365)
c)(65,425)
d)68.22%
e)59.87%.
f)181
g)260
Step-by-step explanation
For normal distribution 68% of the data lie within one standard deviation, 95% within two standard deviations and 99.7% lie within 3 standard deviations
(a)245-60),( 245+60)=(185,305)
b)245-120,245+120=(125,365)
c)245-180, 245+180=(65,425)
d)P(165<X<290)
z1 = -1.333333, z2 = 0.75.
P( 165≤ X ≤ 290 ) = 0.682161
e)P(X<260)
z1 = 0.25
P( X ≤ 260 ) = 0.598706.
f)At 15% x=1.064
x=245-1.064*60
=181.16
g) At 40% x=0.2533
x=245+0.2533*60
=260.198
