Log(x-2)-log (2x-3) = log2
1 answer:
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Answer:
Probability of N Divisible by 3 - 0.33
Probability of N Divisible by 5 - 0.2
Probability of N Divisible by 7 - 0.413
Probability of N Divisible by 15 - 0.066
Probability of N Divisible by 105 - 0.0095
Step-by-step explanation:
Given data:
Integer N {1,2,.....10^3}
Thus total number of ways by which 1000 is divisible by 3 i.e. 1000/3 = 333.3
Probability of N divisible by 3 {N%3 = 0 }
total number of ways by which 1000 is divisible by 5 i.e. 1000/5 = 200
Probability of N divisible by 5 {N%5 = 0 }
total number of ways by which 1000 is divisible by 7 i.e. 1000/7 = 142.857
Probability of N divisible by 7 {N%7 = 0 }
total number of ways by which 1000 is divisible by 15 i.e. 1000/15 = 66.667
Probability of N divisible by 15 {N%15 = 0 }
total number of ways by which 1000 is divisible by 105 i.e. 1000/105 = 9.52
Probability of N divisible by 105 {N%105 = 0 }
similarly for N is selected from 1,2.....(10)^k where K is large then the N value. Therefore effect of k will remain same as previous part.
Answer:
(a) Hence, the margin of error reported by The Marist Poll was correct.
(b) Based on a 95% confidence interval the poll does not provide convincing evidence that more than 70% of the population think that licensed drivers should be required to retake their road test once they turn 65.
Step-by-step explanation:
We are given that the Marist Poll published a report stating that 66% of adults nationally think licensed drivers should be required to retake their road test once they reach 65 years of age.
It was also reported that interviews were conducted on 1,018 American adults, and that the margin of error was 3% using a 95% confidence level.
(a) <u>Margin of error formula is given by;</u>
Margin of Error =
where, = level of significance = 1 - 0.95 = 0.05 or 5%
Standard of error =
Also, = sample proportion of adults nationally think licensed drivers should be required to retake their road test once they reach 65 years of age = 66%
n = sample of American adults = 1.018
The critical value of z for level of significance of 2.5% is 1.96.
So, <em>Margin of Error </em>=
= = 0.03 or 3%
Hence, the margin of error reported by The Marist Poll was correct.
(b) Now, the pivotal quantity for 95% confidence interval for the population proportion who think that licensed drivers should be required to retake their road test once they turn 65 is given by;
P.Q. = ~ N(0,1)
So, <u>95% confidence interval for p</u> =
=
= [0.66 - 0.03 , 0.66 + 0.03]
= [0.63 , 0.69]
Hence, based on a 95% confidence interval the poll does not provide convincing evidence that more than 70% of the population think that licensed drivers should be required to retake their road test once they turn 65 because the interval does not include the value of 70% or more.