Question

4. Suppose the heights of American men are approximately normally distributed with mean of 68 and standard deviation of 2.5. find the percentage of American men who are between 63 to 73 in tall. Given that the percentage of area under the standardized normal curve and hence also under any normal distribution X is as follows: 68.2% for -Iszsl and for u-Osxsu+0, 95.4% for - 2 szs2 and for u-20 sxs u +20, 99.7% for - 3szs3 and for u-30 sxs u +30.

Answer 1

​​​​​​Answer is given according to the Data given in question.

Solution : + iniven data - ( normally distribution) mean (A) = 6 8 Standard deviation = 2.5 C3 +073 is is random Variable x Lie X varging veving from from - Assume that i-e. (35 * $ 73 • and we variable know z that can for be Normally defined clistelbuted as- z = x= a consider z, for x = 63 ; and Z2 for X₂= 73 Noco Z, X- M 6 3-68 - -2 So fy 63 <x< 73 ; & Z will be a {gsoul for -25282} 1-2 sz ça lie. -2 , <a<a the of for a at the range percentage are betweon of American mem (who 63 to 73 in tall) are This is according to the Eriven Amswer will be 95oy %] 95.4%. cuestion data. hence