Question

For the following questions please show all work needed to support your answer. Make sur distributed with a mean of 173.2 cm and a standard deviation of 11 cm. Answer the following questions.
1. Jonathan MathDude discovers that the distribution of heights of students in his class is normally about the distribution of heights for Louis' class:

a. What percent of heights are below 168 cm?
b. What percent of heights lie between 170 cm and 184 cm?
c. What percent of heights lie above 169 cm?

Answer 1

Answer:

0.31821

0.45134

0.6487

Step-by-step explanation:

Given :

Mean (m) = 173.2 cm

Standard deviation (s) = 11 cm

a. What percent of heights are below 168 cm?

P(x < 168)

USing the relation to obtain the standardized score (Z) :

Z = (x - m) / s

Z = (168 - 173.2) / 11

Zscore = −0.472727

p(Z < - 0.4727) = 0.31821 ( Z probability calculator)

b. What percent of heights lie between 170 cm and 184 cm?

P(170 < x < 184)

P(170 - 173.2) / 11) < x < P((184 - 173.3)/11)

P(Z < −0.2909) < P(Z < 0.9818)

P(Z < −0.2909) = 0.38556 (Z probability calculator)

P(Z < 0.9818) = 0.8369 ( Z probability calculator)

0.8369 - 0.38556 = 0.45134

C.) What percent of heights lie above 169 cm

P(x > 169)

Z = (169 - 173.2) / 11

Zscore = −0.381818

p(Z > - 0.3818) = 0.6487 ( Z probability calculator)