Question

A collection of data has a bell shaped, symmetric distribution. The mean of the data is 20 and the standard deviation is 2. Approximately 95% of the data will fall within the interval; [4 points]

[14,26][12,28]    [18,22][16,24][16,26]

Answer 1

Solution :

Given that,

mean = = 20

standard deviation = = 2

Using Empirical rule,

P( - 2 < x <   + 2 ) = 95%

= P( 20 - 2 * 2 < x < 20 + 2 * 2 ) = 95%

= P( 20 - 4 < x < 20 + 4 ) = 95%

=P( 16 < x < 24) = 95%

= [ 16, 24 ]