Question

Question 2. Suppose the mean age of video game players is 28, the standard deviation is 9 years, and the distribution is bell shaped. To assist a video game company’s marketing department in obtaining demographics to increase sales, determine the proportion of players who are

a. between 19 and 28
b. between 28 and 37
c. older than 37

Answer 1

0.34134 ; 0.84134; 0.15866

Step-by-step explanation:

Given that:

Mean (m) = 28

Standard deviation (s) = 9

Proportion of players;

a. between 19 and 28

P(x < 28) - P(x < 19)

Z = (x - mean) / standard deviation

[Z = (28 - 28) / 9] - [Z = (19 - 28) /9]

P(Z < 0) - P(Z < - 1)

0.5 - 0.15866 [Z probability calculator]

= 0.34134

b. between 28 and 37

P(x < 37) - P(x < 28)

Z = (x - mean) / standard deviation

[Z = (37 - 28) / 9] - [Z = (28 - 28) /9]

P(Z < 1) - P(Z < 0)

0.84134 - 0 [Z probability calculator]

= 0.84134

c. older than 37

P(x > 37)

Z = (x - m) / s

Z = (37 - 28) / 9

Z = 9/9 = 1

P(Z > 1) = 1 - P(Z < 1)

P(Z > 1) = 1 - 0.84134

P(Z > 1) = 1 - 0.84134

P(Z > 1) = 0.15866