Question

The accompanying data represent the pulse rates​ (beats per​ minute) of nine students. Treat the nine students as a population. Compute the​ z-scores for all the students. Compute the mean and standard deviation of these​ z-scores.

Student   Pulse
Student 1   77
Student 2   60
Student 3   60
Student 4   80
Student 5   72
Student 6   80
Student 7   80
Student 8   68
Student 9   73

Compute the mean of these​ z-scores.

The mean of the​ z-scores is

​(Round to the nearest tenth as​ needed.)

Compute the standard deviation of these​ z-scores.

The standard deviation of the​ z-scores is
(Round to the nearest tenth as​ needed.)

Answer 1

Formula Ref:

x is a population

Student 1   77

x = 77

mean = 72.2

stdev = 8.1

Z = (x - μ) / σ

z = (77-72.2)/8.1 = 0.59

P(Z < 0.59) = 0.7224

Student 2   60:

Z = -1.51

P(Z< -1.51) = 0.0655

Student 3   60

P(Z< -1.51) = 0.0655

Student 4   80

z = 0.96

P(Z< 0.96) = 0.8315

Student 5   72

z = -0.02

P(Z< -0.02) = 0.4920

Student 6   80

z = 0.96

P(Z< 0.96) = 0.8315

Student 7   80

z = 0.96

P(Z< 0.96) = 0.8315

Student 8   68

Z = -0.52

P(Z < -0.52) = 0.3015

Student 9   73

z = 0.10

P(Z < 0.10) = 0.5398