A hotel maintenance crew wants to estimate how many of the 12,000 lamps in their 30-story hotel need a new light bulb. Which of the following is a random sample of lamps to be inspected?(1 point)
400 lamps on the first 10 floors
all lamps from the rooms with king-sized beds
all lamps in booked rooms
100 lamps on each floor chosen randomly
100 lamps on each floor chosen randomly
Question
A local library manager randomly surveys 80 patrons about the type of book they borrow when they visit the library. The manager finds that 3 patrons borrow novels. If the local library has 345 patrons, approximately how many of them borrow novels when they visit the library? Round your answer to the nearest whole number. (1 point)
To estimate the number of patrons who borrow novels when visiting the library, you can set up a proportion based on the sample surveyed by the manager.
Number of patrons who borrow novels in sample = 3
Total number of patrons in sample = 80
Number of patrons who borrow novels in the entire library = ?
Total number of patrons in the library = 345
Let x be the number of patrons who borrow novels in the entire library.
Using the proportion:
3/80 = x/345
Cross multiply to solve for x:
80x = 3 * 345
80x = 1035
x = 1035 / 80
x ≈ 12.94
Rounded to the nearest whole number, approximately 13 patrons borrow novels when they visit the library.
Use the table to answer the question.
Group A 18 20 46 34 58 31 41
Group B 15 21 32 42 29 57 39
The table shows the times, in minutes, spent shopping by two different groups. First find the mean times each group spent shopping. Then determine the difference in the mean times. Round your answers to one decimal place.(2 points)
The mean time Group A spent shopping is minutes.
The mean time Group B spent shopping is minutes.
The mean times Group A and Group B spent shopping differ by minutes.
To find the mean time spent shopping for each group, follow these steps:
For Group A:
Mean = (18 + 20 + 46 + 34 + 58 + 31 + 41) / 7
Mean = 248 / 7
Mean = 35.43 minutes (rounded to 1 decimal place)
For Group B:
Mean = (15 + 21 + 32 + 42 + 29 + 57 + 39) / 7
Mean = 235 / 7
Mean = 33.57 minutes (rounded to 1 decimal place)
The mean time Group A spent shopping is 35.4 minutes.
The mean time Group B spent shopping is 33.6 minutes.
To find the difference in mean times:
Difference = |35.4 - 33.6|
Difference ≈ 1.8 minutes
The mean times Group A and Group B spent shopping differ by 1.8 minutes.
Which data set has the highest median?(1 point)
{8, 20, 13, 14, 12, 9}
{1, 6, 15, 7, 15, 18, 14}
{11, 15, 16, 8, 12, 14}
{1, 10, 8, 29, 14, 17, 3}
To find the dataset with the highest median, we need to calculate the median of each dataset and compare them.
1. Dataset {8, 20, 13, 14, 12, 9}:
First, sort the data in ascending order: {8, 9, 12, 13, 14, 20}
Since the dataset has an even number of values, the median is the average of the two middle numbers: (12 + 13) / 2 = 12.5
2. Dataset {1, 6, 15, 7, 15, 18, 14}:
First, sort the data in ascending order: {1, 6, 7, 14, 15, 15, 18}
Since the dataset has an odd number of values, the median is the middle number: 14
3. Dataset {11, 15, 16, 8, 12, 14}:
First, sort the data in ascending order: {8, 11, 12, 14, 15, 16}
Since the dataset has an odd number of values, the median is the middle number: 14
4. Dataset {1, 10, 8, 29, 14, 17, 3}:
First, sort the data in ascending order: {1, 3, 8, 10, 14, 17, 29}
Since the dataset has an odd number of values, the median is the middle number: 10
Comparing the medians:
- {8, 20, 13, 14, 12, 9} has a median of 12.5
- {1, 6, 15, 7, 15, 18, 14} has a median of 14
- {11, 15, 16, 8, 12, 14} has a median of 14
- {1, 10, 8, 29, 14, 17, 3} has a median of 10
Therefore, the dataset {1, 6, 15, 7, 15, 18, 14} has the highest median with a value of 14.