Answer:
(53.50 ; 56.75)
127
Step-by-step explanation:
Given the data:
41, 46, 47, 47, 48, 50, 50, 50, 50, 50, 50, 50, 52, 52, 53, 53, 53, 53, 53, 53, 54, 54, 55, 55, 55, 55, 55, 55, 55, 56, 56, 57, 57, 57, 57, 57, 59, 59, 60, 61, 62, 62, 63, 64, 64, 65, 68, 68
Using calculator :
Standard deviation, s = 5.74
Mean, m = 55.125
Sample size, n = 48
95% confidence interval :
Zcritical at 95% = 1.96
Mean ± Zcritical* s/sqrt(n)
55.125 ± 1.96 * 5.74/sqrt(48)
Lower boundary :
55.125 - 1.96(0.8284976) = 53.50
Upper boundary :
55.125 + 1.96(0.8284976) = 56.75
(53.50 ; 56.75)
Sample size, n :
n = [(Zcritical * s) / Error margin]²
Error margin = 1
Zcritical at 95% = 1.96
s = 5.74
n = [(1.96 * 5.74) / 1]²
n = 11.2504²
n = 126.57
n = 127
