B5. (a) Political advisors are interested in whether the electorate is happy wit
ID: 3334478 • Letter: B
Question
B5. (a) Political advisors are interested in whether the electorate is happy with the government or not. They believe the probability a member of the public is i) What is an appropriate binomial probability model for the number of people i) Use a normal approximation to the binomial distribution to calculate the satisfied with the current government is 0.45. They question 180 people who will be satisfied with the current government. probabity that more than 70 people will be satisfied with the current gov- ernment. ii) What are the two assumptions of the binomial model? Are they reasonable here? (b) The normal distribution plays an important role in statistics. Write a very brief commentanswer to each of the following aspects i) the relationship between the mean and the median of the normal distribu- tion i) the 68 -95- 99.7 rule; ii) the use of normal probability plots, with reference to the two examples below Probability Plot of C31 Probability Plot of C33 iv) the Central Limit TheoremExplanation / Answer
(a1) binomial with parameter n=180 and p=0.45
(a ii) for binomial mean=np=0.45*180=81 and standard deviation=sd=sqrt(np(1-p))=sqrt(180*0.45*(1-0.45))=6.67
for x=70, z=(x-mean)/sd=(70-81)/6.67=-1.6492
required probability=P(x>70)=P(z>-1.6492)=1-P(z<-1.6492)=1-0.05=0.95
(a iii) the assumptions are: (1) The number of trials, n, is fixed. (2) There are two and only two outcomes, labelled as "success" and "failure"
(b1) mean and median of normal distribution are equal
(b2) In statistics, the 68–95–99.7 rule is a shorthand used to remember the percentage of values that lie within a band around the mean in a normal distribution with a width of two, four and six standard deviations, respectively; more accurately, 68.27%, 95.45% and 99.73% of the values lie within one, two and three standard deviations of the mean, respectively.
(b3) didnot understand the question, although first plot is right for normal probability plot
(b4) The central limit theorem (CLT) is a statistical theory that states that given a sufficiently large sample size from a population with a finite level of variance, the mean of all samples from the same population will be approximately equal to the mean of the population. It establishes that, in most situations, when independent random variables are added, their properly normalized sum tends toward a normal distribution (informally a "bell curve") even if the original variables themselves are not normally distributed.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.