Answer:
a) P [Z < 5.79] = 7.49 %
b) P [ Z > 7.46 ] = 82.38 %
c) P [ Z > 6.65 ] = 91.68 %
Step-by-step explanation:
Normal Distribution
Population Mean μ₀ = 6.8 cm
Standard Deviation of population σ = 0,7 cm
a) P [ Z < 5.79 ] = ??
z value ?
z = ( 5,79 - 6,8 ) / 0,7 ⇒ z = - 1.01 / 0,7 ⇒ z = - 1.442
From z table we get:
z = - 1.442 ⇒ P [Z < 5.79] = 0.0749 or
P [Z < 5.79] = 7.49 %
b) P [ Z > 7.46 ]
z = ( 7.46 - 6,8 ) / 0,7 ⇒ z = 0.66 / 0.7 ⇒ z = 0.942
From z table
P [ Z > 7.46 ] = 0.8238 or P [ Z > 7.46 ] = 82.38 %
c) P [ Z > 6.65]
z = ( 6.65 - 6.8 ) / 0.7 ⇒ z = - 0,15 / 0.7 ⇒ z = - 0.214
From table we get area between 6.65 and the mean, therefore we have to add ( 0.5 ) half of total area
Then from z table
z = - 0,214 ⇒ 0,4168
Then P [ Z > 6.65 ] = 0,4168 + 0.5
P [ Z > 6.65 ] = 0.9168 or
P [ Z > 6.65 ] = 91.68 %
P [ Z > 6,65 ] = 0,5 +
