Question

(2 points) Suppose we have a normally-distributed population that has a mean of 65 and a standard deviation of 5. 5. (a) What percent of observations will fall in the interval from 55 to 75? (Hint: Find out how many standard deviations the range spans on both sides of the mean and use the 68/95/99.5 rule) (b) What percent of observations will fall in the interval from 60 to 70?

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Answer #1

a) here as k score=(X-mean)/std deviation

therefore P(55<X<75)=P((55-65)/5<Z<(75-65)/5)=P(-2<Z<2) =95%

b)

P(60<X<70)=P((60-65)/5<Z<(70-65)/5)=P(-1<Z<1) =68.0%

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