In: Math
As in exercise 3 Cholesterol levels in health us adults average about 215mg/Dl with a Standard deviation of about 30 mg /dl and are roughly normally distributed If the cholestrol levels of a sample of 42 healthy us adults is taken what is the probablility that the mean cholesterol level of the sample
A. will be no more than 215?
b. will be between 205 and 225
c. Will be less than 200?
d. Will be greater than 220?
a)
µ = 215
σ = 30
n= 42
X = 215.00
Z = (X - µ )/(σ/√n) = ( 215
- 215 ) / ( 30 /
√ 42 ) = 0.000
P(X ≤ 215 ) = P(Z ≤
0.000 ) = 0.5000
excel formula for probability from z score is
=NORMSDIST(Z)
.....
b)
µ = 215
σ = 30
n= 42
we need to calculate probability for ,
205 ≤ X ≤ 225
X1 = 205 , X2 =
225
Z1 = (X1 - µ )/(σ/√n) = ( 205
- 215 ) / ( 30 /
√ 42 ) = -2.16
Z2 = (X2 - µ )/(σ/√n) = ( 225
- 215 ) / ( 30 /
√ 42 ) = 2.16
P ( 205 < X <
225 ) = P ( -2.16
< Z < 2.16 )
= P ( Z < 2.16 ) - P ( Z
< -2.16 ) =
0.98462 - 0.01538 =
0.96925
excel formula for probability from z score is
=NORMSDIST(Z)
c)
µ = 215
σ = 30
n= 42
X = 200.00
Z = (X - µ )/(σ/√n) = ( 200
- 215 ) / ( 30 /
√ 42 ) = -3.240
P(X ≤ 200 ) = P(Z ≤
-3.240 ) = 0.0006
excel formula for probability from z score is
=NORMSDIST(Z)
.
d)
µ = 215
σ = 30
n= 42
X = 220
Z = (X - µ )/(σ/√n) = ( 220
- 215 ) / ( 30 /
√ 42 ) = 1.1
P(X ≥ 220 ) = P(Z ≥
1.08 ) = P ( Z <
-1.080 ) = 0.1400
excel formula for probability from z score is
=NORMSDIST(Z)