Question

Students taking an introductory statistics class reported spending...

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.

Answer & Explanation
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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