Answer
(a) 84.13%
(b) 61.47%
(c) 77.34%
(d) 22.66%
(e) 20.38%
(f) 20.38%
Work Step by Step
You will need this formula
$z = (y - μ) / σ $
Where
y = the point of intrest
μ = the mean of the data set
σ = the standard deviation of the data set
*Please refer to table 3 for the Standard Normal Cumulative Probability Table
The brain weights of a certain population of adult Swedish males follow approximately a normal distribution with mean 1,400 gm and standard deviation 100 gm.
What percentage of the brain weights are
(a) 1,500 gm or less
$1 = (1500 - 1400) / 100 $
1 on the Standard Normal Cumulative Probability Table is 0.8413
(b) between 1,325 and 1,500 gm?
$1= (1500 - 1400) / 100 $
$-0.75 = (1325 - 1400) / 100 $
1 = 0.8413
-0.75 = 0.2266
$0.8413 - 0.2266 = 0.6147$
(c) 1,325 gm or more?
$-0.75 = (1325 - 1400) / 100$
$-0.75 = 0.2266$
$1 - 0.2266 = 0.7734$
(d) 1,475 gm or more?
$0.75 = (1475 - 1400) / 100 $
$0.75 = 0.7734$
$1 - 0.7734 = 0.2266$
(e) between 1,475 and 1,600 gm?
$0.75 = (1475 - 1400) / 100 $
$2 = (1600 - 1400) / 100 $
$2 = 0.9772$
$0.75 = 0.7734$
$0.9772 - 0.7734 = 0.2038$
(f) between 1,200 and 1,325 gm?
$-2 = (1200 - 1400) / 100 $
$-0.75 = (1325 - 1400) / 100 $
$-2 = 0.0228$
$-0.75 = 0.2266$
$0.2266 - 0.0228 = 0.2038$
