Question

In: Statistics and Probability

Apply the 68-95-99.7 Rule to a mean of 67.9498 and standard deviation 1.94

Expert Solution

Solution :

Given that,

mean = = 67.9498

standard deviation = = 1.94

Using Empirical rule,

a) P( - < x < + ) = 68%

= P( 67.9498 - 1.94< x < 67.9498 + 1.94 ) = 68%

= P( 66.0098 < x < 69.8898 ) =68%

b) P( - 2 < x < + 2 ) = 95%

= P( 67.9498 - 2 * 1.94 < x < 67.9498 + 2 * 1.94 ) = 95%

= P( 67.9498 - 3.88 < x < 67.9498 + 3.88 ) = 95%

=P( 64.0698 < x < 71.8298 ) = 95%

c) P( - 3< x < + 3 ) = 99.7%

= P( 67.9498 - 3 * 1.94 < x < 67.9498 + 3 * 1.94 ) = 99.7%

= P( 67.9498 - 5.82 < x < 67.9498 + 5.82 ) = 99.7%

=P( 62.1298 < x < 73.7698 ) = 99.7%

orchestra answered 2 years ago

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