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For each of the questions below, a histogram is described. Indicate in each case whether, in...

For each of the questions below, a histogram is described. Indicate in each case whether, in view of the Central Limit Theorem, you can be confident that the histogram would look like approximately a bell-shaped (normal) curve, and give a brief explanation why (one sentence is probably sufficient).

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.

Solutions

Expert Solution

1.

The histogram would look like approximately a bell-shaped curve.

Price of most of the days will be near to the mean of the prices of 365 days. Very few will be far both in positive and negative sides.

2.

The histogram would look like approximately a bell-shaped curve.

Mean number of heads obtained by the students should be near to 20 (assuming unbiased coins). Most of the observed data will be close to this value and few may lie far.

3.

The histogram would look like approximately a bell-shaped curve.

Mean of the sum recorded by the students should be close to 60*(1+6)/2=210 (assuming unbiased die). Most of the observed data will be close to this value and few may lie far.

4.

The histogram would not look like a bell-shaped curve. It might be a positively skewed curve.

In practice, we observe lot of people possessing average salaries as well as a lot of them possessing lower salaries whereas a few having higher salaries.

5.

The histogram would look like approximately a bell-shaped curve.

Most of the observed values by different polling organisations will lie near to the mean of number of votes for the Democratic candidate recorded by polling organizations and a few may lie far.

6.

The histogram would look like approximately a bell-shaped curve.

Most of the average ages recorded by the polling organizations will near to the combined average age and few may lie far.

7.

The histogram would look like approximately a bell-shaped curve.

Most of the values of lifetime of batteries would lie near the mean value of the lifetime of batteries and very few may lie further.

milcah answered 10 months ago
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