In a large statistics class,the professor has each student toss a coin 58 times and calculate the proportion of his or her tosses that were tails.The students then report their results,and the professor plots a histogram of these several proportions.Should a Normal model be used here?
A)A Normal model should be used because the samples are random and independent.Also,the sample size,58,is less than 10% of the population.Most importantly,the original population has a Normal distribution.
B)A Normal model should be used because the 58 coin tosses can be thought of as a random sample of coin tosses and are fewer than 10% of the population of all coins.The success/failure condition is also satisfied because np = 29 ≥ 10 and nq = 29 ≥ 10.
C)A Normal model should not be used because the sample size is not large enough to satisfy the success/failure condition.
D)A Normal model should not be used because the sample size,58,is larger than 10% of the population of all coins.
E)A Normal model should not be used because the population distribution is not Normal.

Question

Quizplus · Accepted Answer

A Normal model should be used because the sample size, 58, is less than 10% of the population of all coins. Also, the success/failure condition is satisfied because np=29 ≥ 10 and nq=29 ≥ 10. This means we can consider the proportion of tails as a sample proportion from a binomial distribution, which can be approximated by a Normal distribution.

In a Large Statistics Class,the Professor Has Each Student Toss