Questions: The hours of sleep that citizens get on a typical night is shown in the table to the right. A researcher in sleep deprivation finds that the average human needs at least six hours a night to function property. What is the probability of a citizen getting at least six hours of sleep a night? Hours of Sleep Number of Citizens, in millions --- --- 4 or less 14 5 13 6 76 7 93 8 87 9 10 10 or more 7 Total 300 The chance of finding a citizen who gets at least six hours of sleep is %.

The hours of sleep that citizens get on a typical night is shown in the table to the right. A researcher in sleep deprivation finds that the average human needs at least six hours a night to function property. What is the probability of a citizen getting at least six hours of sleep a night?

Hours of Sleep Number of Citizens, in millions
--- ---
4 or less 14
5 13
6 76
7 93
8 87
9 10
10 or more 7
Total 300

The chance of finding a citizen who gets at least six hours of sleep is %.

Transcript text: The hours of sleep that citzens get on a typical night is shown in the table to the right. A researcher in sleep deprivation finds that the average human needs at least six hours a night to function property. What is the probability of a citizen getting at least six hours of sleep a night? \begin{tabular}{|l|c|} \hline \begin{tabular}{c} Hours of \\ Sleep \end{tabular} & \begin{tabular}{c} Number \\ of Citizens, in \\ millions \end{tabular} \\ \hline 4 or less & 14 \\ \hline 5 & 13 \\ \hline 6 & 76 \\ \hline 7 & 93 \\ \hline 8 & 87 \\ \hline 9 & 10 \\ \hline 10 or more & 7 \\ \hline & Total 300 \\ \hline \end{tabular} The chance of finding a citizen who gets at least six hours of sleep is $\square$ \%.

Solution

Solution Steps

Step 1: Summarize the Given Data

We are given the number of citizens (in millions) who get different amounts of sleep per night. The data is as follows:

\[ \begin{array}{|c|c|} \hline \text{Hours of Sleep} & \text{Number of Citizens (millions)} \\ \hline 4 \text{ or less} & 14 \\ \hline 5 & 13 \\ \hline 6 & 76 \\ \hline 7 & 93 \\ \hline 8 & 87 \\ \hline 9 & 10 \\ \hline 10 \text{ or more} & 7 \\ \hline \end{array} \]

The total number of citizens is 300 million.

Step 2: Calculate the Number of Citizens Getting at Least 6 Hours of Sleep

To find the number of citizens who get at least 6 hours of sleep, we sum the number of citizens in the categories of 6 hours or more:

\[ 76 + 93 + 87 + 10 + 7 = 273 \text{ million} \]

Step 3: Calculate the Probability

The probability $ P $ of a citizen getting at least 6 hours of sleep is given by the ratio of the number of citizens getting at least 6 hours of sleep to the total number of citizens:

\[ P = \frac{273}{300} \]

Step 4: Convert the Probability to a Percentage

To express the probability as a percentage, we multiply by 100:

\[ P \times 100 = \left( \frac{273}{300} \right) \times 100 = 91\% \]