WorksheetsCentral Limit Theorem
Total questions: 11
Worksheet time: 3hrs 45mins
Name
Class
Date
1.
The mean and standard deviation of a population are 400 and 40, respectively. Sample size is 25.
What is the mean of the sampling distribution?
What is the mean of the sampling distribution?
a)
400
b)
40
c)
25
d)
8
2.
The mean and standard deviation of a population are 400 and 40, respectively. Sample size is 25.
What is the standard error of the sampling distribution?
What is the standard error of the sampling distribution?
a)
400
b)
40
c)
25
d)
8
3.
A group of 625 students has a mean age of 15.8 years with a standard deviation of 0.6 years. The ages are normally distributed. What is the probability that a randomly selected student is older than 16.5 years old?
a)
0.864
b)
0.879
c)
0.121
d)
None of these
4.
The amount of fuel used by jumbo jets to take off is normally distributed with a mean of 4000 gallons and a standard deviation of 125 gallons. What is the probability that the mean number of gallons of fuel needed to take off for a randomly selected sample of 40 jumbo jets will be less than 3950 gallons?
a)
.0057
b)
.025
c)
.345
d)
.781
5.
Researches found that boys playing high school football absorb an average of 355 hits to the head with a standard deviation of 80 hits during a season. What is the probability on a randomly selected team of 48 players that the average number of head hits per player is between 340 and 360?
a)
.236
b)
.429
c)
.571
d)
.614
6.
True or False:
The mean of the sample means is equal to the mean of the population.
a)
True
b)
False
7.
True or False:
The variance of the sampling distribution is equal to the population variance multiplied by the sample size.
a)
True
b)
False
8.
State whether you would use the central limit theorem or the normal distribution:
The weights of the eggs produced by a certain breed of hen are normally distributed with mean 65 grams and standard deviation of 5 grams.
What is the probability that one egg selected at random from a hen house will weigh more than 68 grams?
The weights of the eggs produced by a certain breed of hen are normally distributed with mean 65 grams and standard deviation of 5 grams.
What is the probability that one egg selected at random from a hen house will weigh more than 68 grams?
a)
Central Limit Theorem
b)
Normal Distribution
9.
State whether you would use the central limit theorem or the normal distribution:
The weights of the eggs produced by a certain breed of hen are normally distributed with mean 65 grams and standard deviation of 5 grams.
What is the probability that the average weight of a dozen eggs selected at random will be more than 68 grams?
The weights of the eggs produced by a certain breed of hen are normally distributed with mean 65 grams and standard deviation of 5 grams.
What is the probability that the average weight of a dozen eggs selected at random will be more than 68 grams?
a)
Central Limit Theorem
b)
Normal Distribution
10.
State whether you would use the central limit theorem or the normal distribution:
In a study done on the life expectancy of 500 people in a certain geographic region, the mean age at death was 72 years and the standard deviation was 5.3 years.
If a sample of 50 people from this region is selected, and the probability that the mean life expectancy will be less than 70 years.
In a study done on the life expectancy of 500 people in a certain geographic region, the mean age at death was 72 years and the standard deviation was 5.3 years.
If a sample of 50 people from this region is selected, and the probability that the mean life expectancy will be less than 70 years.
a)
Central Limit Theorem
b)
Normal Distribution
11.
In your own words, give a situation in the real-world where a person would choose to use the Central Limit Theorem as a tool for evaluating that situation. Only a well-articulated response will receive credit.
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