For condition 1, there exists a population with a fixed proportion with a certain trait. For condition 2, a random sample of students is selected. For condition 3, the sample size of 200 is large enough that we indeed likely to see at least five right-handed and five left handed students.
Problem 2.
Bell shaped with a mean of 0.12 and a standard deviation of 0.023.
Problem 5.
Possible sample means are bell-shaped with a mean of 25 and standard deviation of 1/3, so 68% are between 24.7 and 25.3, 95% are between 24.4 and 25.6 and almost all are between 24.1 and 25.9.
Problem 6.
The picture is more compact. The mean is still 25, but the standard deviation is 0.1.
Problem 9.
Yes, The Rule for Sample Proportions (the Central Limit Theorem) tells us that the distribution of sample proportions would be normal with a mean of 0.6 and a standard deviation of 0.049. Therefore 95% of the time the sample proportion would be within 2 standard deviations of 0.6, or be between 0.502 and .698. So there is very small probability (less than 2.5%) that the sample proportion would fall below .50. As long as the sample proportion fell above 50%, there would be convincing evidence that the quarter system is favored. Another way to see this is to compute the standardized score for a proportion of .5; it would be (.5 - .6)/0.49 = 2.04. That lies at the 2nd percentile, meaning that a value below 50% would occur only with a probability of 0.02.
Problem 10.
a) The SD = 0.003. Almost all sample proportions are likely to be within 3 SD of the true proportion, which is about 0.009, or just under 1%.
b) The proportion in 1976 is likely to be within 1% of the true proportion for that time period, indicating that it is between 8% and 10%. The value of 25% in 1997 far exceeds this range, so it is likely to represent a real increase in the proportion of all adults who believe in reincarnation.
Problem 13.
a)The distribution is normal with a mean of 6.95 hours and standard deviation of 0.15 hours.
b) Yes the mean of 7.1 hours is about 1 SD above the mean of the possible values for sample means based on 190 people, so it is well within the range of what is expected.
c) The sample is unlikely to be representative of all adults. There are many ways in which college students differ from all adults in factor regarding sleep.
Problem 14.
a)This random sample does not meet the criteria of condition 3, because the sample size is not large enough. Even if the sample did show that exactly 10% of the cars did meet the emission standards, this would be only 3, not the required minimum of 5.
b) This meets all of the conditions.
c) This sample violates condition 1. It would not be random, and the relative frequency of rain or snow changes from the winter months to the summer months.
d) This meets all of the conditions.
Problem 15.
a) It does not apply because the sample is not random; he biased it by using only heart attack patients.
b) Again this is probably a biased sample, so the rule does not apply. People who leave during that time may be different in their responses from people who work late.
c) Incomes are not bell-shaped, but this is a large enough sample so that the rule applies (as long as the university is careful to contact the particular people chosen to be in the sample). The population under consideration is alumni and the measurement of interest is income.
d) the rule would not apply here because the sales prices are not likely to be bell shaped and the sample is small.
Problem 18.
The want the 3 standard deviations to equal 1, where a single standard deviation is 5/sqrt(n). so they need n= 15^2 or 225.