Answer:
Step-by-step explanation:
Hello!
The vairable of interest is
X: number of drivers, out of 80 drivers traveling the interstate, that exceded the speed limit.
n= 80
p=0.40
This variable is discrete and has a normal distribution. The conditions that should be met to apply the CLT and approximate the sampling distribution to normal are:
n≥30 ⇒ Check
n*p≥5 ⇒ 80*0.40= 32 Check
n*q≥5 ⇒ 80*0.6= 48 Check
All conditions are met then ^p≈N(p*;(pq)/n)
a) Using the 68-95-99.7 rule, draw and label the distribution of the proportion of these cars the police will observe speeding. Which graph shows the distribution of the proportion with the intervals for 68%, 95%, and 99.7%.
The mean of the distribution is p= 0.4
The standard deviation of the distribution is √[(pq)/n]= √[(0.4*0.6)/80]= 0.05
Empirical rule:
μ-σ≤0.66≤μ+σ ⇒ 0.4-0.05 ≤0.66≤ 0.4*0.05 ⇒ 0.35 ≤0.66≤ 0.45
μ-2σ≤0.95≤μ+2σ ⇒ 0.4-0.1≤0.95≤0.4+0.1 ⇒ 0.3≤0.95≤0.5
μ-3σ≤0.997≤μ+3σ ⇒ 0.4-0.15≤0.997≤0.4+0.15 ⇒ 0.25≤0.997≤0.55
See graphic in attachment.
b) Do you think the appropriate conditions necessary for your analysis are met? Are the conditions necessary to use a normal model met?
1. yes all conditions are met
2. no the randomization and 10% conditions are met.
3. no the 10% condition is not met
4. no the randomization condition is not met
5. no the randomization and success/failure conditions are not met
6. no the success/failure condition is not met
7. no the 10% and success/failure conditions are not met8. no none of the conditions are met
