3. In order to use the normal distribution to approximate probabilities of propo

Question

3. In order to use the normal distribution to approximate probabilities of proportions, which of the following needs to be true: A. np 2 10 B. np 30 C. np 2 10& nq2 10 D. nq10 We can always use the 4. According to a recent Suppose we randomly select 180 adults and find 59% ofthe sam when riding a bike. Which of the following correctly desc of adults in the sample who never wear a helmet when riding a bike? survey, 53% ofadults say they never wearahelmet when riding aa helmet ple say they never wear a helmet ribes the distribution for the proportion A. AN (0.53, 0.0372) B. X AN(95.4, 6.6961) p AN(0.59,0.0367) D. AN (0.53,0.0014) E. None of the above.

Explanation / Answer

c. for the approximation, the population size should be atleast 10 larger than the sample size. Thus by central limit theorem np>= 10 and nq>=10

d. the proportion of population approximately follows normal distribution with mean = p and sd = sqrt(p(1-p)/N)

mean p = 0.53 and sd = sqrt(0.53*0.47/180) = 0.0372

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