Question

In: Statistics and Probability

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). There are no data for these questions, so you will not need to use the computer to answer these questions.

A police department records the number of 911 calls made each day of the year, and the 365 values are plotted in a histogram.

The day before an election, fifty different polling organizations each sample 500 people and record the percentage who say they will vote for the Democratic candidate. The 50 values are plotted in a histogram.

The fifty polling organizations also record the average age of the 500 people in their sample, and the 50 averages are plotted in a histogram.

One hundred batteries are tested, and the lifetimes of the batteries are plotted in a histogram.

Two hundred students in a statistics class each flip a coin 50 times and record the number of heads. The numbers of heads are plotted in a histogram.

Two hundred students in a statistics each roll a die 40 times and record the sum of the numbers they got on the 40 rolls. They make a histogram of the 200 sums.

One thousand randomly chosen people report their annual salaries, and these salaries are plotted in a histogram.

Solutions

Expert Solution

(1)

A police department.....:   We cannot be confident that the histogram would look like approximately a bell - shaped (normal) curve because the actual population values are plotted and not the average values of samples.

(2)

The day before election....:   We cannot be confident that the histogram would look like approximately a bell - shaped (normal) curve because the actual population values are plotted and not the average values of samples.

(3)

The fifty polling organizations....:   We can be confident that the histogram would look like approximately a bell - shaped (normal) curve because the average age values are plotted.

(4)

One hundred batteries...: We cannot be confident that the histogram would look like approximately a bell - shaped (normal) curve because the actual population values are plotted and not the average values of samples.

(5)

Two hundred students... We cannot be confident that the histogram would look like approximately a bell - shaped (normal) curve because the actual population values are plotted and not the average values of samples.

(6)

Two hundred students....:   We cannot be confident that the histogram would look like approximately a bell - shaped (normal) curve because the actual population values are plotted and not the average values of samples.

(7)

One thousand randomly chosen people...:   We cannot be confident that the histogram would look like approximately a bell - shaped (normal) curve because the actual population values are plotted and not the average values of samples.

orchestra answered 2 years ago
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