Measures of Center
What is the mode?
the number that occurs most often in a data set
Sketch the region of a normal distribution represented by the probability statement:
P(z<2.2)
(show on board)
Which z-value is used for a 95% confidence interval?
1.96
The track team runs a short race with the following time results (in minutes): 3.2, 3.1, 3.5, 4, 3.9, 3.6, 3.1, 3.5
Pretend one of the runners tripped and fell during the race, and ended up with a time of 4.3 instead of his usual 3.9. How would the standard deviation change?
It would increase
What is the median for this data set?
7, 10, 3, 3, 1, 12, 5, 4, 2, 7, 8
5
Use the standard normal curve to calculate the probability:
P(Z>1.41)
0.0793
True or False: The more confident you want to be in a study, the larger your confidence level must be.
True
Put the following steps to calculate standard deviation (of a sample) in order:
a) take the square root
b) find the difference between each data value and the mean
c) calculate the mean
d) square each value
e) add up those new values
f) divide by n -1
1) calculate the mean
2) find the difference between each data value and the mean
3) square each value
4) add up those new values
5) divide by n -1
6) take the square root
For an original data set:
7, 10, 3, 3, 1, 12, 5, 4, 2, 7, 8
The additional data point, 13, is added. What effect will this have on the mean? The median? The mode?
The mean will increase.
The median will also increase.
The mode will stay the same.
The height of women is normally distributed with an average height of 64 inches and a standard deviation of 2.5 inches. If a woman is selected a random, what is the probability that she is less than 60 inches tall?
0.0548
Which of the following changes to a study would result a larger margin of error? That is, you would be less certain of the results.
a) increasing the sample size
b) increasing the confidence level
c) decreasing the sample size
c) decreasing the sample size
What is the corresponding z-score for x = 82 for a normal distributed population with a mean of 96 and a standard deviation of 8?
-1.75
20 students taking Math 107 were asked how many time they use AI to help them during one homework assignment, and the mean was found to be 2.5 times. One of the students lied: He said he used AI 2 times, but he actually used it 8 times. With this info, what is the actual mean?
2.8
Calculate the value of c:
P(-c < z < c) = 0.885
c = 1.2
We plan to survey college seniors to see what proportion plan to attend grad school next year. Using 98% confidence, how many students should we survey if we wish the margin of error to be within 3%?
approximately 1500
Calculate the standard deviation for the following data:
7, 10, 3, 3, 1, 12, 5, 4, 2, 7, 8
3.47