Question

For a population with a normal distribution with mean 23.5 and a standard deviation 2.6​, determine the following. ​

(a) About​ 68% of the population lies between what​ limits? ​

(b) About​ 95% of the population lies between what​ limits?

​(c) About​ 99.7% of the population lies between what​ limits

Answer 1

Solution :

Given that,

= 23.5

= 1.5

Using Empirical rule,

(A)P( - 1< X < + 1) = 68%

P(23.5 - 2.6< X < 23.5 + 2.6) = 68%

P(20.9 < X < 26.1) = 68%

Answer = 20.9 and 26.1

(B)

P( - 2< X < + 2) = 95%

P(23.5 -5.2< X < 23.5 + 5.2) = 95%

P(18.3< X < 28.7) =95%

Answer = 18.3 and 28.7

(C)

P( - 3< X < + 3) =99.7%

P(23.5 -7.8< X < 23.5 + 7.8) = 99.7%

P(15.7< X <31.3) =99.7%

Answer = 15.7and 31.3