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?
A
400 lamps on the first 10 floors
B
all lamps in booked rooms
C
all lamps from the rooms with king-sized beds
D
100 lamps on each floor chosen randomly
D
100 lamps on each floor chosen randomly
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 from the survey borrow novels. If the local library has 345 patrons, approximately how many of them borrow novels when they visit the library? (HINT: It might be helpful to set up a proportion to solve.)
Round your answer to the nearest whole number.
patrons
To find out approximately how many of the 345 patrons borrow novels, we can set up a proportion using the information given.
Let x represent the number of patrons who borrow novels out of the 345 total patrons.
We can set up the proportion:
3/80 = x/345
Cross multiplying, we get:
80x = 3 * 345
80x = 1035
Dividing both sides by 80:
x = 1035 / 80
x ≈ 12.94
Rounded to the nearest whole number, approximately 13 patrons borrow novels when they visit the library.
These are the scores for two randomly selected lacrosse teams. Find the range of the number of goals scored by each team. Based on the range, which team has a more consistent number of goals scored?
Lacrosse Team 1: 6 0 4 17 3 12
Lacrosse Team 2: 23 14 22 14 17
22
The range for Lacrosse Team 1 is
The range for Lacrosse Team 2 is
Based on the range, Lacrosse Team ________
has a more consistent number of goals scored.
The range of a set of numbers is found by subtracting the smallest number from the largest number.
For Lacrosse Team 1:
Range = 17 - 0 = 17
For Lacrosse Team 2:
Range = 23 - 14 = 9
Based on the range, Lacrosse Team 2 has a more consistent number of goals scored, as their range is smaller.
Given the data set: 5, 10, 12, 14, 18, 60
Which of the following statements is true regarding this data?
A
The value 60 is the outlier
B
No outliers exist
C
The value 5 is the outlier.
D
Multiple outliers exist.
To identify outliers, we need to determine if any values in the dataset are significantly different from the other values. One common rule is that any value beyond 1.5 times the interquartile range (IQR) can be considered an outlier.
First, let's order the numbers in the dataset from least to greatest: 5, 10, 12, 14, 18, 60.
Next, we calculate the IQR:
1. Find the median (middle value): 12
2. Find the lower quartile (median of lower half): (10 + 12) / 2 = 11
3. Find the upper quartile (median of upper half): (14 + 18) / 2 = 16
4. Calculate the IQR: 16 - 11 = 5
Now, we can calculate the fences to identify potential outliers:
1. Lower Fence: Q1 - 1.5 * IQR = 11 - 1.5 * 5 = 3.5
2. Upper Fence: Q3 + 1.5 * IQR = 16 + 1.5 * 5 = 23.5
Looking at the dataset, we see that all values fall within the range of 3.5 to 23.5, so there are no outliers.
Therefore, the correct statement is:
B
No outliers exist.
you sure?
Apologies for the confusion. My previous response was incorrect.
Given the dataset: 5, 10, 12, 14, 18, 60
To identify outliers, we can calculate the z-score for each data point. The z-score measures how far a particular value is from the mean in terms of standard deviations.
First, we calculate the mean:
Mean = (5 + 10 + 12 + 14 + 18 + 60) / 6 = 21.5
Next, we calculate the standard deviation:
Standard Deviation = sqrt(((5-21.5)^2 + (10-21.5)^2 + (12-21.5)^2 + (14-21.5)^2 + (18-21.5)^2 + (60-21.5)^2)/6) = 20.34
Now, let's calculate the z-score for each data point:
z-score for 5 = (5 - 21.5) / 20.34 = -0.81
z-score for 10 = (10 - 21.5) / 20.34 = -0.57
z-score for 12 = (12 - 21.5) / 20.34 = -0.47
z-score for 14 = (14 - 21.5) / 20.34 = -0.37
z-score for 18 = (18 - 21.5) / 20.34 = -0.17
z-score for 60 = (60 - 21.5) / 20.34 = 1.89
From the calculations, we can see that the value 60 has a z-score of 1.89. Any value with a z-score greater than 1.96 or less than -1.96 is considered an outlier. Since 1.89 does not exceed this threshold, it is not considered an outlier.
Therefore, the correct statement is:
B
No outliers exist.
The data set shown below has an outlier. Determine the outlier and then fill out the chart.
Data: 5, 10, 12, 14, 18, 24, 60
If the outlier is excluded, what happens to:
Increase
Decrease
No effect
A
the median?
B
the mean?
C
the mode?
D
the range?