Suppose the distribution of the heights of students from college A has bell-shap

Question

Suppose the distribution of the heights of students from college A has bell-shaped with mean 168 cm and standard deviation 10. Find the following:

a). What’s the percentage of students whose heights are two deviations above or below the mean? And percentage of students whose heights are three deviations above or below the mean? b). What’s percentage of students whose heights are above 178 cm?

c). Suppose, we do not know any information about the distribution of the heights of students from college A (i.e. we don’t know if it is bell shaped or not), what percentage of students whose heights is within 3 standard deviations within the mean (3 standard deviations above and below the mean) ?

Explanation / Answer

from empriical rule

a)percentage of students whose heights are two deviations above or below the mean =95.45%

percentage of students whose heights are three deviations above or below the mean =99.73%

b) percentage of students whose heights are above 178 cm =P(X>178)=1-P(X<178)=1-P(Z<1)=1-0.8413=0.1587

or 15.87%

c) for distribution not known from Chebychev's ;

percentage of students whose heights is within 3 standard deviations within the mean =(1-1/k2)*100

=(1-1/32)*100 =88.89%

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.