Answer:
0.12995
0.47508
0.0841
0.738
Step-by-step explanation:
Given that:
Percentage of STEM (p) = 27% = 0.27
Sample size (n) = 47
Using Normal approximation :
Mean (m) = n*p = 47 * 0.27 = 12.69
Standard deviation (s) = √(n*p*q)
q = 1 - p = 1 - 0.27 = 0.73
Standard deviation (s) = √(47*0.27*0.73) = 3.04
a. Exactly 13 of them major in STEM.
P(12.5 < x < 13.5)
USing the z formula :
(x - m) / s
(12.5 - 12.69) / 3.04 < x (13.5 - 12.69) / 3.04
-0.0625 < z < 0.2664
Using the z probability calculator:
P(Z < - 0.0625) = 0.47508
P(Z < 0.2664) = 0.60503
0.60503 - 0.47508
= 0.12995
b. At most 12 of them major in STEM.
P(X ≤ 12.5)
Zscore = (x - m) / s
Zscore = (12.5 - 12.69) / 3.04
Zscore = −0.0625
P(Z ≤ - 0.0625) = 0.47508
c. At least 9 of them major in STEM.
P(X ≥ 8.5)
Zscore = (x - m) / s
Zscore = (8.5 - 12.69) / 3.04
Zscore = −1.378
P(Z ≤ - 1.378) = 0.0841
d. Between 8 and 15 (including 8 and 15) of them major in STEM.
(8.5 - 12.69) / 3.04 < x (15.5 - 12.69) / 3.04
-1.378 ≤ z ≤ 0.924
Using the z probability calculator:
P(Z ≤ 0.924) = 0.82226
P(Z ≤ - 1.378) = 0.084102
0.82226 - 0.084102
= 0.738
