Ramos Barrett

06/17/2023 · Elementary School

Since \( \mu = 75 \) and \( \sigma = 8 \) we have:  \( P ( X > 75 ) = P ( X - \mu > 75 - 75 ) = P ( \frac { X - \mu } { \sigma } > \frac { 75 - 75 } { 8 } ) \) Since \( Z = \frac { x - \mu } { \sigma } \) and \( \frac { 75 - 75 } { 8 } = 0 \) we have: \( P ( X > 75 ) = P ( Z > 0 ) \) Step 3: Use the standard normal table to conclude that: \( P ( Z > 0 ) = 0.5\) Note: Visit the Z - score calculator for a step by step explanation on how to use the standard normal table. Since \( \mu = 75 \) and \( \sigma = 8 \) we have: \( P ( X > 91 ) = P ( X - \mu > 91 - 75 ) = P ( \frac { X - \mu } { \sigma } > \frac { 91 - 75 } { 8 } ) \) Since \( Z = \frac { x - \mu } { \sigma } \) and \( \frac { 91 - 75 } { 8 } = 2 \) we have: \( P ( X > 91 ) = P ( Z > 2 ) \) Step 3: Use the standard normal table to conclude that: \( P ( Z > 2 ) = 0.0228\)