In: Statistics and Probability
Solution :
Given that ,
mean = = 84.2
standard deviation = = 4.8
n = 31
a) = = 84.2
= / n = 4.8 / 31 = 0.86
b) P( < 86 ) = P(( - ) / < ( 86 - 84.2) / 0.86 )
= P(z < 2.09 )
Using z table
= 0.9817
c) P( > 85 ) = 1 - P( < 85 )
= 1 - P[( - ) / < ( 85 - 84.2) / 0.86 ]
= 1 - P(z < 0.93 )
Using z table
= 1 - 0.8238
= 0.1762
d) P( 83.5 < < 85.5 )
= P[( 83.5 - 84.2 ) / 0.86 < ( - ) / < ( 85.5 - 84.2 ) / 0.86 )]
= P( -0.81 < Z < 1.51 )
= P(Z < 1.51 ) - P(Z < -0.81 )
Using z table
= 0.9345 - 0.2090
=0.7255