Question

A distribution of numbers is approximately bell-shaped. If the mean of the numbers is 129 and the standard deviation is 15,

a. between what two numbers would approximately 68% of the values fall?
between

_____ and ______

b. Between what two numbers would 95% of the values fall?
between

_____ and _______

c. Between what two values would 99.7% of the values fall?
between

______ and ______

Answer 1

Solution :

Given that,

Using Empirical rule,

(A)P(129 - 1(15)< X < 129 + 1(15))=68%

P(114< X < 144) = 68%

answer =114<and 144

(B)P(129 - 2(15)< X < 129 + 2(15)) = 95%

P(99< X <159) = 99.7%

answer 99 and 159

(C)P(129 - 3(15)< X < 129 + 3(15))= 99.7%

P(84< X < 174) = 99.7%

answer 84 and 174