Question

Study 1: the mean of 75 and a standard deviation of 10. Study 2: mean of 75, standard deviation of 3. which has the higher probability for P(70<x<80)

Answer 1

For study 1:

Given,

= 75, = 10

We convert this to standard normal as

P( X < x) = P( Z < x - / )

P( 70 < X < 80) = P( X < 80) - p( X < 70)

= P( Z < 80 - 75 / 10) - P (Z < 70 - 75 / 10)

= P( Z < 0.5) - P (Z < -0.5)

= 0.6915 - ( 1 - 0.6915)

= 0.3830

For Study 2

= 75, = 3

P( 70 < X < 80) = P( X < 80) - p( X < 70)

= P( Z < 80 - 75 / 3) - P (Z < 70 - 75 / 3)

= P( Z < 1.6667) - P (Z < -1.6667)

= 0.9522 - ( 1 - 0.9522)

= 0.9044

For study 2 with lower standard deviation has the higher probability for P( 70 < X < 80)