Answer:
a) From the empirical rule we know that about 68% of the samples are between:
[tex]\mu_p -\sigma = 0.7-0.0512=0.6488[/tex]
[tex]\mu_p +\sigma = 0.7+0.0512=0.7512[/tex]
95% of the sample proportions would be between:
[tex]\mu_p -2\sigma = 0.7-2*0.0512=0.5976[/tex]
[tex]\mu_p +2\sigma = 0.7+2*0.0512=0.8024[/tex]
And 99.7 % would be between these limits:
[tex]\mu_p -3\sigma = 0.7-3*0.0512=0.5464[/tex]
[tex]\mu_p +3\sigma = 0.7+3*0.0512=0.8536[/tex]
And the figure attached explain the results obtained.
b) i) Independence condition of all the cars
ii) np>10 , 80*0.7=56>10
n(1-p)= 80(1-0.7)=24>10
We have all the conditions so then the normal model can be used.
Step-by-step explanation:
Part a
For this case we assume that the true parameter of interest on this case is p= proportion of drivers traveling on a major interstate highway exceeding the spped limit. For this case the mean and the deviation for the proportion is given by:
[tex]\mu_p = 0.7[/tex]
[tex]\sigma_p =\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.7(1-0.7)}{80}}=0.0512[/tex]
From the empirical rule we know that about 68% of the samples are between:
[tex]\mu_p -\sigma = 0.7-0.0512=0.6488[/tex]
[tex]\mu_p +\sigma = 0.7+0.0512=0.7512[/tex]
95% of the sample proportions would be between:
[tex]\mu_p -2\sigma = 0.7-2*0.0512=0.5976[/tex]
[tex]\mu_p +2\sigma = 0.7+2*0.0512=0.8024[/tex]
And 99.7 % would be between these limits:
[tex]\mu_p -3\sigma = 0.7-3*0.0512=0.5464[/tex]
[tex]\mu_p +3\sigma = 0.7+3*0.0512=0.8536[/tex]
And the figure attached explain the results obtained.
b) Do you think the appropriate conditions necessary for your analysis are met? Explain.
We assume the following conditions:
i) Independence condition of all the cars
ii) np>10 , 80*0.7=56>10
n(1-p)= 80(1-0.7)=24>10
We have all the conditions so then the normal model can be used.
