Percentiles
The 70th and 80th percentiles of a set of scores are 78 and 86, respectively; the interquartile range of the scores is 41. Which of these scores is more likely than the others to be at the 25th percentile?
What is 40
Explanation:
The interquartile range of a set of scores is the difference between the third and first quartile - that is, the difference between the 75th and 25th percentiles. The 75th percentile is between 78 and 86, so, if 41 is subtracted from those numbers, the upper and lower bounds of the 25th percentile can be found.
P70<P75<P80
P70−IR<P75−IR<P80−IR
P70−IR<P25<P80−IR
78−41<P25<86−41
37<P25<45
Of our choices, only 40 falls in this range.
Scores on a history test have average of 80 with standard deviation of 6. What is the z-score for a student who earned a 75 on the test?
What is -0.833
Explanation:
The z-score of (75 - 80)/6 and is equal to -0.833.
The height of plants in a certain garden are normally distributed with a mean of 38.3 inches and a standard deviation of 5.3 inches.
Use the Empirical Rule to estimate what percentage of plants are greater than 48.9 inches tall.
What is 2.5%
Explanation:
The Empirical Rule states that for a given dataset with a normal distribution, 95% of data values fall within two standard deviations of the mean. This means that 47.5% of values fall between the mean and two standard deviations above the mean.
In this example, 48.9 is located two standard deviations above the mean. Since we know that 50% of data values fall below the mean in a normal distribution, a total of 50% + 47.5% = 97.5% of values fall below 48.9. This means that 100% - 97.5% = 2.5% of values fall above 48.9.
Thus, 2.5% of plants are greater than 48.9 inches tall.
Where is Japan
What is the probability of getting a sum of 5,6,or7 when rolling two six-sided fair dice?
Possible Answers:
7/12
5/9
5/12
1/2
4/9
What is 5/12
Explanation:
The sample space, or total possible outcomes, when rolling two six-sided dice is 36.
Ways to get what you want:
5:1,42,33,24,1
6:1,52,43,34,25,1
7:1,62,53,44,35,26,1
So there are 15 ways to get a 5,6,or7.
So the probability becomes 15/36=5/12
The weight of chocolate bars from a particular chocolate factory has a mean of 8 ounces with standard deviation of .1 ounce. What is the z-score corresponding to a weight of 8.17 ounces?
What is 1.7
Explanation:
The z-score for this problem is (8.17 - 8)/.1 and is equal to 1.7.
The height of plants in a certain garden are normally distributed with a mean of 40.5 inches and a standard deviation of 3.2 inches.
Use the Empirical Rule to estimate what percentage of plants are greater than 34.1 inches tall.
What is 97.5%
Explanation:
The Empirical Rule states that for a given dataset with a normal distribution, 95% of data values fall within two standard deviations of the mean. This means that 47.5% of values fall between the mean and two standard deviations below the mean.
In this example, 34.1 is located two standard deviations below the mean. Since we know that 50% of data values fall above the mean in a normal distribution, a total of 50% + 47.5% = 97.5% of values fall above 34.1.
Thus, 97.5% of plants are greater than 34.1 inches tall.
What is Koala
Q2 is the median of the overall data set. Q1 is the median of the lower half of the data set. Q3 is the median of the upper half of the data set.
Find the interquartile range (Q3−Q1) for the following data set:
23,45,32,29,37,47,21,36,52
Possible Answers:
26
20
36
31
46
What is 20
Explanation:
First, put the data set in order from smallest to largest:
21,23,29,32,36,37,45,47,52
Q2=36 which is the middle number in the data set.
Q1=26 which is the average of the two middle numbers of the lower half of the data set.
Q3=46 which is the average of the two middle numbers of the upper half of the data set.
Thus the interquartile range is Q3−Q1=46−26=20
Note, the range of the data set is given by the largest number minus the smallest number, or 52−21=31
What is-2.7
Explanation:
The height of plants in a certain garden are normally distributed with a mean of 36.3 inches and a standard deviation of 4.8 inches.
Use the Empirical Rule to estimate what percentage of plants are less than 31.5 inches tall.
What is 16%
Explanation:
The Empirical Rule states that for a given dataset with a normal distribution, 68% of data values fall within one standard deviation of the mean. This means that 34% of values fall between the mean and one standard deviation below the mean.
In this example, 31.5 is located one standard deviation below the mean. Since we know that 50% of data values fall above the mean in a normal distribution, a total of 50% + 34% = 84% of values fall above 31.5. This means that 100% - 84% = 16% of values fall below 31.5.
Thus, 16% of plants are less than 31.5 inches tall.
What is Egyptians
Marjorie was excited to learn that her baby was in the 10th percentile for weight at his doctor's appointment. She posted on social media exclaiming that her baby was in the top 10% of all babies his age in weight, meaning that he is a very large baby! Is Marjorie's interpretation correct? If not, explain what the 10th percentile for weight means.
What is Incorrect?
Explanation:
The 10th percentile means that 10% of the data occurs below this value and 90% occurs above this value. Therefore, Marjorie was incorrect in her interpretation. Her baby being in the 10th percentile for weight means that only 10% of babies his age weigh less than he does. This means that 90% of babies his age are larger in weight.
The temperature is recorded at 60 airports in a region. The average temperature is 67 degrees Fahrenheit with standard deviation of 5 degrees. What is the z-score for a temperature of 68 degrees?
What is 0.2
Explanation:
Here the number of airports is information that is not necessary to solve the problem. The z-score for this problem is (68-67)/5 and is equal to 0.2.
The height of plants in a certain garden are normally distributed with a mean of 37.8 inches and a standard deviation of 4.6 inches.
Use the Empirical Rule to estimate what percentage of plants are greater than 51.6 inches tall.
What is 0.15%
Explanation:
The Empirical Rule states that for a given dataset with a normal distribution, 99.7% of data values fall within three standard deviations of the mean. This means that 49.85% of values fall between the mean and three standard deviations above the mean.
In this example, 51.6 is located three standard deviations above the mean. Since we know that 50% of data values fall below the mean in a normal distribution, a total of 50% + 49.85% = 99.85% of values fall below 51.6. This means that 100% - 99.85% = 0.15% of values fall above 51.6.
Thus, 0.15% of plants are greater than 51.6 inches tall.
What is 1995