Quiz #1- Distribution of Means/Central Limit Theorem

The distribution of a population has a population mean of 4 and a population standard deviation of 2.5. If samples of size 25 (n =25) were taken from the population what would be the mean of the sample means?  $M_{x̄}=$  

• 0.8

• 1.5

• 4

• 6.5

The distribution of a population has a population mean of 2.5 and a population standard deviation of 3. If samples of size 36 (n =36) were taken from the population what would be the standard deviation of the sample means?  $\sigma_{x̄}=$  

• 0.083

• 0.500

• 1.200

• 3.000

Use the central limit theorem if possible. For a sample of n = 36, find the probability of a sample mean being greater than 43 given  $\mu=42$    and  $\sigma=12$  . The population is also normally distributed.

• 0.3085

• 0.4668

• 0.5332

• 0.6915

The length of pregnancies are normally distributed with a mean of 268 days  $\mu=268$    and a standard deviation of 15 days  $\sigma=15$  . A group of 36 pregnant women (n=36) were in a parenting class together. What is the probability that the average pregnancy for the women lasted longer than 270 days?

• 21.2%

• 28.8%

• 55.2%

• 78.8%

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?

• Central Limit Theorem
• Normal Distribution

Tags

CCSS.HSS.ID.A.4

CCSS.HSS.ID.A.2

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.ID.A.4

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.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

What happens to the shape of a sampling distribution of sample means as n increases?

• The skew gets bigger

• The skew is reversed

• It becomes narrower and more normal.

• The shape is the same, but wider

True or False: The central limit theorem states that the sampling distribution of the expected values (means) of a population with a mean of  $\mu$    and a standard deviation of  $\sigma$   will be approximately normal for any population regardless of the shape of the underlying population if the sample is large enough (n>30)

• True 

• False