Answer:
Step-by-step explanation:
Given the following :
Mean ( m) = 2.98
Standard deviation (sd) = 0.05
A) proportion of cases with mean less than 3.014 inches
X = 3.014
Zscore = (x - m) / sd
Zscore = (3.014 - 2.98) / 0.05
= 0.034 / 0.05
= 0.68
P(Z < 0.68) ; from z table = 0.7517
B.)
25th percentile (0.25) = Q1; corresponds to a Zscore of about - 0.675
Zscore = (x - m) / sd
-0.675 = (X - 2.98) / 0.05
-0.675 * 0.05 = X - 2.98
-0.03375 = X - 2.98
X = 2.946 = 2.95
C)
Q3 = 0.75
75th percentile (0.75) ; corresponds to a Zscore of about 0.675
Zscore = (x - m) / sd
0.675 = (X - 2.98) / 0.05
0.675 * 0.05 = X - 2.98
0.03375 = X - 2.98
0.03375 + 2.98 = X
X = 3.01
IQR = Q3 - Q1
IQR = 3.01 - 2.95 = 0.06
Lower outlier :
Q1 - 1.5(IQR) = 2.95 - 1.5(0.06) = 2.86
UPPER OUTLIER:
Q3 + 1.5(IQR) = 3.01 + 1.5(0.06) = 3.10
Proportion less than 2.86:
Z = (2.86 - 2.98) / 0.05
= - 0.12 / 0.05
= - 2.4
P(Z < 2.4) = 0.0082
Proportion < 3.10
Z = (3.1 - 2.98) / 0.05
= 0.12 / 0.05
= 2.4
P(Z > 2. 4) = 1 - P(Z < 2.4) = (1 - 0.9918) = 0.0082
Proportion of
