Answer:
1. 564 tractor trailers
2. (0.2919, 0.4339)
3. It should be noted that there is 90% confidence that the true population proportion lies between 0.2919 and 0.4339.
Step-by-step explanation:
1)
Proportion= P = 0.8333333333333 (1/12)
Margin error= 0.06/2 = 0.03
Confidence level= 99
Significance level = α= (100 - 99)%= 1%= 0.01
α/2 = 0.01/2 = 0.0005
Sample size= n
= p(1 - p) (Z*/E)
=0.8333333333333 x (2.576/0.03)^2
=563.15
Approximately
=564
2) Sample size n= 124
Sample number of event x =45
Sample proportion = p= x/n
=45/124
= 0.3629
Standard error =√p(1 - p) /n
√(0.3629× (1 - 0.3629)/ 124
= 0.0432
Confidence level= 90
Significance level α= (100-90)% =0.01
Critical value Z* = 1.645
Margin of error = Z×Standard error= 1.645 × 0.0432= 0.07103
Lower limit = p- margin error= 0.3629 - 0.07103= 0.2919
Upper limit = p+margin error= 0.3629 + 0.07103= 0.4339
The answer is (0.2919, 0.4339)
3) It should be noted that there is 90% confidence that the true population proportion lies between 0.2919 and 0.4339.
