Answer
(a) 97.98%
(b) 12.71%
(c) 46.39%
(d) 10.69%
(e) 35.51%
(f) 5.59%
(g) 59.10%
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 heights of a certain population of corn plants follow a normal distribution with mean 145 cm and standard deviation 22 cm. What percentage of the plants heights are
(a) 100 cm or more?
$-2.05=(100−145)/22$
$-2.05 = 0.0202$
$1 - 0.0202 = 0.9798$
(b) 120 cm or less?
$-1.14=(120−145)/22$
$-1.14 = 0.1271$
(c) between 120 and 150 cm?
$-1.14=(120−145)/22$
$0.23=(150−145)/22$
$0.23 = 0.5910$
$-1.14 = 0.1271$
$0.5910 - 0.1271 = 0.4639$
(d) between 100 and 120 cm?
$-1.14=(120−145)/22$
$-2.05=(100−145)/22$
$-2.05 = 0.0202$
$-1.14 = 0.1271$
$0.1271 - 0.0202 = 0.1069$
(e) between 150 and 180 cm?
$0.23=(150−145)/22$
$1.59=(180−145)/22$
$1.59 = 0.9441$
$0.23 = 0.5910$
$0.9441 - 0.5910 = 0.3551$
(f) 180 cm or more?
$1.59=(180−145)/22$
$1.59 = 0.9441$
$1 - 0.9441 = 0.0559$
(g) 150 cm or less?
$0.23=(150−145)/22$
$0.23 = 0.5910$
