Central Limit Theorem

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?

• 400
• 40
• 25
• 8

Tags

CCSS.HSS.MD.A.2

CCSS.HSS.MD.A.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?

• 0.864
• 0.879
• 0.121
• None of these

Tags

CCSS.HSS.ID.A.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?

• .0057
• .025
• .345
• .781

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

CCSS.HSS.ID.A.4

CCSS.HSS.MD.A.2

CCSS.HSS.MD.A.3

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?

• .236
• .429
• .571
• .614

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

CCSS.HSS.ID.A.4

True or False:

The mean of the sample means is equal to the mean of the population.

• True

• False

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

True or False:

The variance of the sampling distribution is equal to the population variance multiplied by the sample size.

• True

• False

Tags

CCSS.HSS.IC.A.1

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?

• Central Limit Theorem
• Normal Distribution

Tags

CCSS.HSS.ID.A.2

CCSS.HSS.ID.A.4

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? 

• Central Limit Theorem
• Normal Distribution

Tags

CCSS.HSS.ID.A.4

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.

• Central Limit Theorem
• Normal Distribution

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

CCSS.HSS.ID.A.4

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.

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.3

CCSS.HSS.IC.B.4

CCSS.HSS.ID.A.4