Attributes of Central Limit Theorem (Challenge Problems)
100
The population has a mean of 14 and a standard deviation of 3. What is the sample standard deviation for a group n = 25?
s = 0.6
100
The population has a mean of 14 and a standard deviation of 3. How many samples must be drawn to reduce the standard deviation to 1?
N = 9
100
The population has a mean of 14 and a standard deviation of 3. What is the probability that someone in a SAMPLE group of 25 people will score a 16 or below?
Report s, z-score, and probability.
s = 0.6
z = 3.33
p = 99.96%
100
The mean of the population is ____________ to the mean of the sample
equal
200
The population has a mean of 30 and a standard deviation of 6.
What is the mean of the sample?
What is the sample standard deviation for a group N = 49
s = 0.86
200
The population has a mean of 30 and a standard deviation of 6. How many samples must be drawn to reduce the sample standard deviation to 3?
N = 4
200
The population has a mean of 30 and a standard deviation of 6. What is the probability that someone in a SAMPLE group of 36 people will score a 27 or below?
Report s, z-score, and probability.
s = 1
z = -3.00
p = 0.13%
200
a low standard deviation tells you scores are ____________ _______________
close together
300
The population has a mean of 120 and a standard deviation of 12.
What is the mean of the sample?
What is the sample standard deviation for a group N = 36
s = 2
300
The population has a mean of 120 and a standard deviation of 12. How large of a sample is needed to reduce the sample standard deviation to 4?
N = 9
300
The population has a mean of 120 and a standard deviation of 12. What is the probability that someone in a SAMPLE group of 36 people will score a 123 or above?
Report s, z-score, and probability.
s = 2
z = 1.50
p = 6.68%
300
a high standard deviation tells you scores are ____________ _______________
far apart
400
The class average on a quiz was an 88% with a standard deviation of 5. What is the sample standard deviation for a group of 10 students?
s = 1.58
400
The class average on a quiz was an 88% with a standard deviation of 5. How many students would you need to sample to reduce the standard deviation to 0.5?
N = 100
400
The class average on a quiz was an 88% with a standard deviation of 5. What is the probability that someone in a SAMPLE group of 36 people will score a 90% or above?
Report s, z-score, and probability.
s = 0.83
z = 2.41
p = 0.8%
400
What happens to the sample standard deviation as the sample size increases?
what happens to s as n increases?
the sample standard deviation decreases
500
The average number of hours a high schooler sleeps at night is 8 hours with a standard deviation of 1.2 hours. What is the sample standard deviation for a group of 100 high schoolers?
s = 0.12
500
The average number of hours a high schooler sleeps at night is 8 hours with a standard deviation of 1.2 hours. How many high schoolers would you need to survey to reduce the sample standard deviation to 0.5?
N = 5.76
500
The average number of hours a high schooler sleeps at night is 8 hours with a standard deviation of 1.2 hours. What is the probability that someone in a SAMPLE group of 9 people will sleep more than 9 hours?
Report s, z-score, and probability.
s = 0.4
z = 2.5
p = 0.62%
500
The distribution of _________________ is ____________ ________________