Question

distribution of scores for a certain standardized test is a normal distribution with a mean of 4 75 and the standard deviation of 30
between what two values would you expect to find about 68%

between what two values would you expect to find about 99.7%

Answer 1

Solution :

Given that,

mean = = 475

standard deviation = = 30

Using Empirical rule,

a) P( - < x <   + ) = 68%

= P( 475 - 30 < x < 475 + 30 ) = 68%

= P( 445 < x < 505 ) =68%

b) P( - 3 < x <   + 3 ) = 99.7%

= P( 475 - 3 * 30 < x < 475 + 3 * 30 ) = 99.7%

= P( 475 - 90 < x < 475 + 90 ) = 99.7%

=P( 385 < x < 565 ) = 99.7%