For each of the questions below, a histogram is described. Indicate in each case
ID: 3171210 • Letter: F
Question
For each of the questions below, a histogram is described. Indicate in each case whether you think the histogram should look like approximately a bell-shaped (normal) curve, and give a brief explanation why (one sentence is probably sufficient). There are no data for these questions, so you will not need to use the computer to answer these questions.
Recall also that individual observations could have many different distributions (such as binomial, geometric, Poisson, exponential, uniform, or normal). If we make a histogram of data that come from, say, an exponential distribution, then the histogram will show an exponential shape, not a normal distribution, regardless of how many observations there are. Only averages (and therefore sums) of large numbers of observations are guaranteed to have approximately a normal distribution by the Central Limit Theorem.
1. The price of one gallon of gasoline at a particular gas station is recorded every day of the year, and the 365 values are plotted in a histogram.
2. Two hundred students in a statistics class each flip a coin 40 times and record the number of heads. The numbers of heads are plotted in a histogram.
3. Two hundred students in a statistics each roll a die 60 times and record the sum of the numbers they got on the 60 rolls. They make a histogram of the 200 sums.
4. One thousand randomly chosen people report their annual salaries, and these salaries are plotted in a histogram.
5. The day before an election, fifty different polling organizations each sample 2000 people and record the percentage who say they will vote for the Democratic candidate. The 50 values are plotted in a histogram.
6. The fifty polling organizations also record the average age of the 2000 people in their sample, and the 50 averages are plotted in a histogram.
7. One hundred batteries are tested, and the lifetimes of the batteries are plotted in a histogram.
Explanation / Answer
Correct cases:
Case nos. 3 & 6 only.
REASON:
By Central Limit Theorem, only averages ( and therefore sums) oflarge number of observations are gaurenteed to have approximately normal distribution(
Thus,
Case 1: not an average or sum: 365 values of price - So, not normal distribution
Case 2: not an average or sum: 200 number of heads - So, not normal distribution
Case 4: not an average or sum: 1000 salaries - So, not normal distribution
Case 5: not an average or sum: 50 percentages - So, not normal distribution.
Case 7: not average or sum.100 life times - So, not normal distribution.
Correct cases:
Case no. 3: sum: 200 sums of the numbers. - So, normal distribution.
Case no. 6: average: 50 averages _ so, normal distribution
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.