Question
The manager at a water park constructed the following frequency distribution to summarize attendance in July and August.
Attendance Frequency
1,000 < x ≤ 1,250 7
1,250 < x ≤ 1,500 11
1,500 < x ≤ 1,750 17
1,750 < x ≤ 2,000 5
2,000 < x ≤ 2,250 4
2,250 < x ≤ 2,500 6
a-1. Construct the relative frequency distribution and the cumulative relative frequency distribution (Round your answers to 2 decimal places.)
a-2. What proportion of the time was attendance more than 1,500 but no more than 1,750 people? (Round your answer to 2 decimal places.)
a-3. What proportion of the time was attendance 1,250 or less? (Round your answer to 2 decimal places.)
a-4. What proportion of the time was attendance more than 1,250 people? (Round your answer to 2 decimal places.)
b. Which statement is correct regarding the shape of the distribution using a histogram?
multiple choice
The distribution is symmetric.
The distribution is not symmetric.
Attendance Frequency
1,000 < x ≤ 1,250 7
1,250 < x ≤ 1,500 11
1,500 < x ≤ 1,750 17
1,750 < x ≤ 2,000 5
2,000 < x ≤ 2,250 4
2,250 < x ≤ 2,500 6
a-1. Construct the relative frequency distribution and the cumulative relative frequency distribution (Round your answers to 2 decimal places.)
a-2. What proportion of the time was attendance more than 1,500 but no more than 1,750 people? (Round your answer to 2 decimal places.)
a-3. What proportion of the time was attendance 1,250 or less? (Round your answer to 2 decimal places.)
a-4. What proportion of the time was attendance more than 1,250 people? (Round your answer to 2 decimal places.)
b. Which statement is correct regarding the shape of the distribution using a histogram?
multiple choice
The distribution is symmetric.
The distribution is not symmetric.
Answers
Answered by
GPT 3.5
a-1. To construct the relative frequency distribution, divide each frequency by the total number of observations (sum of all frequencies). To construct the cumulative relative frequency distribution, add up the relative frequencies for each category, starting from the lowest category.
Attendance Range Frequency Relative Frequency Cumulative Relative Frequency
1,000 < x ≤ 1,250 7 0.14 0.14
1,250 < x ≤ 1,500 11 0.22 0.36
1,500 < x ≤ 1,750 17 0.34 0.70
1,750 < x ≤ 2,000 5 0.10 0.80
2,000 < x ≤ 2,250 4 0.08 0.88
2,250 < x ≤ 2,500 6 0.12 1.00
a-2. The proportion of the time attendance was more than 1,500 but no more than 1,750 people is the relative frequency for that category, which is 0.34.
a-3. The proportion of the time attendance was 1,250 or less can be calculated by adding up the relative frequencies for the first two categories: 0.14 + 0.22 = 0.36.
a-4. The proportion of the time attendance was more than 1,250 people can be calculated by subtracting the proportion of the time attendance was 1,250 or less (0.36) from 1: 1 - 0.36 = 0.64.
b. The statement "The distribution is not symmetric" is correct regarding the shape of the distribution using a histogram.
Attendance Range Frequency Relative Frequency Cumulative Relative Frequency
1,000 < x ≤ 1,250 7 0.14 0.14
1,250 < x ≤ 1,500 11 0.22 0.36
1,500 < x ≤ 1,750 17 0.34 0.70
1,750 < x ≤ 2,000 5 0.10 0.80
2,000 < x ≤ 2,250 4 0.08 0.88
2,250 < x ≤ 2,500 6 0.12 1.00
a-2. The proportion of the time attendance was more than 1,500 but no more than 1,750 people is the relative frequency for that category, which is 0.34.
a-3. The proportion of the time attendance was 1,250 or less can be calculated by adding up the relative frequencies for the first two categories: 0.14 + 0.22 = 0.36.
a-4. The proportion of the time attendance was more than 1,250 people can be calculated by subtracting the proportion of the time attendance was 1,250 or less (0.36) from 1: 1 - 0.36 = 0.64.
b. The statement "The distribution is not symmetric" is correct regarding the shape of the distribution using a histogram.