Free Printable sampling distribution and central limit theorem

1.

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

a)

It becomes narrower and bimodal.

b)

It becomes narrower and more normal.

c)

It becomes wider and skewed right.

d)

It becomes wider and more normal.

2.

These symbols represent the mean and standard deviation for which of the following distributions?

a)

The Population

b)

The Sample

c)

The Sampling Distribution

3.

These symbols represent the mean and standard deviation for which of the following distributions?

a)

The Population

b)

The Sample

c)

The Sampling Distribution

4.

These symbols represent the mean and standard deviation for which of the following distributions?

a)

The Population

b)

The Sample

c)

The Sampling Distribution

5.

The mean and standard deviation of a population are 200 and 20, respectively. Sample size is 25.
What is the mean of the sampling distribution?

a)

200

b)

16

c)

25

d)

4

6.

The mean and standard deviation of a population are 200 and 20, respectively. Sample size is 25.
What is the standard deviation of the sampling distribution?

a)

200

b)

16

c)

25

d)

4

7.

Taxi fares in New York City are normally distributed with a mean fare of $22.50 and a standard deviation of $2.20. A tourism agency surveys 25 of its clients who have recently traveled to New York City to determine whether or not this information is accurate.

The mean of the sampling distribution for average taxi fare where the sample size is 25 is (a) .

8.

Taxi fares in New York City are normally distributed with a mean fare of $22.50 and a standard deviation of $2.20. A tourism agency surveys 25 of its clients who have recently traveled to New York City to determine whether or not this information is accurate.

The standard deviation of the sampling distribution for average taxi fare where the sample size is 25 is (a) .

9.

Taxi fares in New York City are normally distributed with a mean fare of $22.50 and a standard deviation of $2.20. A tourism agency surveys 25 of its clients who have recently traveled to New York City to determine whether or not this information is accurate.

Your best friend just got back from New York and says she had a taxi fare of $25.00. What is the z-score that would correspond to his/her taxi fare?

a)

-1.14

b)

1.14

c)

-5.68

d)

5.68

10.

Taxi fares in New York City are normally distributed with a mean fare of $22.50 and a standard deviation of $2.20. A tourism agency surveys 25 of its clients who have recently traveled to New York City to determine whether or not this information is accurate.

The sample of 25 tourists reported an average taxi fare of $23.20. What is the z-score that corresponds to this amount?

a)

-0.318

b)

0.318

c)

-1.59

d)

1.59

11.

Taxi fares in New York City are normally distributed with a mean fare of $22.50 and a standard deviation of $2.20. A tourism agency surveys 25 of its clients who have recently traveled to New York City to determine whether or not this information is accurate.

Recently a sample of 25 tourists reported an average taxi fare of $23.20. What is the probability that a sample of 25 would have an average taxi fare greater than $23.20 ?

a)

.3752

b)

.6248

c)

.0559

d)

.9441

12.

The average speed of 1500 vehicles traveled on a stretch of highway that day is 67 miles per hour with a standard deviation of 3.5 miles per hour. If 100 vehicles are randomly selected as samples, what would be the mean of the resulting sampling distribution of sample means?

a)

63.5

b)

67

c)

70.5

d)

74

13.

The standard deviation of a sampling distribution is the same as the standard deviation as the population.

a)

True

b)

False

14.

The mean of the sampling distribution is the same as the mean of the population.

a)

True

b)

False

15.

If $\mu\ =\ 100$ and $\sigma\ =\ 15$ and repeated samples of size 10 are taken, what are the mean and standard deviation of the sampling distribution?

a)

$\mu_x=\ 100$ and $\sigma_x\ =\ 15$

b)

$null$ and $\sigma_{\ x}\ =\ \frac{\sqrt{15}}{10}$

c)

$null$ and $\sigma_{x\ }=\frac{15}{\sqrt{10}}$

d)

$\mu_{x\ }=\ \frac{15}{\sqrt{10}}$ and $\sigma_{x\ }=\ 100$

16.

What is the purpose of using a random method to get a sample?

a)

A. Reduce bias.

b)

B. Reduce variability.

c)

C. Increase bias.

d)

D. Increase variability.

17.

The mean weight of potato chip bags is 10.5 ounces with a standard deviation of 3 ounces. A random sample of 40 bags of potato chips is selected. What is the probability that the mean of the sample is less than 10 ounces?

a)

-1.05

b)

.146

c)

.020

d)

.853

18.

The mean distance an OHS student travels to school is 5.6 miles with a standard deviation of 1.7 miles. Mrs. McLemore finds the mean of her 4th period class - a randomly selected sample of 39 students. What is the probability that the mean of her class is more than 6 miles?

a)

0.002

b)

0.070

c)

0.898

d)

1.27

19.

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

20.

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

21.

Suppose the teenagers that attend public high schools get an average of 5.7 hours of sleep each night with a standard deviation of 1.7 hours. What is the probability that a randomly selected group of 35 high school students get more than 6 hours of sleep each night?

a)

.430

b)

.148

c)

.281

d)

.087

22.

For the population of farm workers in New Zealand, suppose that weekly income has a distribution with a mean of µ = $500 and a standard deviation of σ = $160. A survey of 100 farm workers is taken, including information on their weekly income.

What is the probability that a randomly selected worker has an income of at most $530?

a)

0.0304

b)

0.9696

c)

0.4591

d)

0.318

e)

~0

23.

In the formula shown above, what does N stands for?

a)

sample size

b)

population size

c)

number of respondents

d)

number 30

24.

What is the equivalent value of the standard deviation of the sampling distribution of the sample means in comparison to the standard deviation in a finite population?

a)

b)

25.

Which of the following symbol describes the population mean?

a)

$\mu$

b)

$n$

c)

$x̄$

d)

$σ$

26.

The population mean age of the residents in a certain city is 56.12 years with a standard deviation of 15.3 years. A group of 2000 residents from a certain barangay in the city is taken as a sample. If the population of the city 150 000, find the mean of the sampling distribution of the sample mean of the residents’ ages.

a)

150 000

b)

2 000

c)

15.3

d)

56.12

27.

The population mean age of the residents in a certain city is 56.12 years with a standard deviation of 15.3 years. A group of 2000 residents from a certain barangay in the city is taken as a sample. If the population of the city 150 000, find the standard deviation of the sampling distribution of the sample mean of the residents’ ages.

a)

150 000

b)

0.34

c)

0.5

d)

56.12

28.

In a survey of a sample of high school students, 43% said that their mother has taught them the most about managing money.

a)

parameter

b)

statistic

29.

Sixty-two of the 97 passengers aboard the Hindenburg airship survived its explosion.

a)

parameter

b)

statistic

30.

A restaurant chain wanted to find out how the customer experience was in a store.
Which choice best represents a statistic?

a)

The percentage of all customers that reported a positive experience.

b)

The percentage of customers surveyed that reported a positive experience.

c)

All customers.

d)

A random selection of customers that were surveyed.

31.

A survey company was trying to see if people in a state thought the pollution was too high.
Which choice best represents a parameter?

a)

All people in the state.

b)

Percentage of all people in the state who thought the pollution was too high.

c)

500 randomly selected residents of the state.

d)

71% of the residents surveyed thought the pollution was too high.

32.

Lee will conduct a survey at his school. He will select a random sample of students at the school to take the survey. Which sample is the best random sample for Lee to use?

a)

every other student in the drama club

b)

every fifth student who enters the school

c)

every student who rides the same bus as Lee

d)

every fourth student in Lee’s homeroom class

33.

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

a)

It becomes narrower and bimodal.

b)

It becomes narrower and more normal.

c)

It becomes wider and skewed right.

d)

It becomes wider and more normal.

34.

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?

a)

400

b)

40

c)

25

d)

8

35.

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?

a)

400

b)

40

c)

25

d)

8

36.

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

37.

These symbols represent the mean and standard deviation for which of the following distributions?

a)

The Population

b)

The Sample

c)

The Sampling Distribution

38.

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

39.

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

40.

Suppose the teenagers that attend public high schools get an average of 5.7 hours of sleep each night with a standard deviation of 1.7 hours. What is the probability that a randomly selected group of 35 high school students get more than 6 hours of sleep each night?

a)

.430

b)

.148

c)

.281

d)

.087

41.

True or False:

As the sample size n increases without limit, the shape of the distribution becomes less normal.

a)

True

b)

False

42.

True or False:

The number of samples for sampling with replacement may be computed by multiplying the sample size to the population size.

a)

True

b)

False

43.

True or False:

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

a)

True

b)

False

44.

True or False:

Whatever is the distribution of the population if sample size is increased, the distribution will become approximately normal.

a)

True

b)

False

45.

True or False:

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

a)

True

b)

False

46.

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?

a)

Central Limit Theorem

b)

Normal Distribution

47.

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?

a)

Central Limit Theorem

b)

Normal Distribution

48.

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.

a)

Central Limit Theorem

b)

Normal Distribution

49.

What is the relationship between the mean of the population and the mean of the sampling distribution of the sample means?

a)

the mean of the population is greater than the mean of the sampling distribution of the sample means.

b)

the mean of the population is lesser than the mean of the sampling distribution of the sample means.

c)

the mean of the population is equal to the mean of the sampling distribution of the sample means.

d)

the mean of the population is not equal to the mean of the sampling distribution of the sample means.

50.

What is the equivalent value of the standard deviation of the sampling distribution of the sample means in comparison to the standard deviation in an infinite population?

a)

b)

51.

What is the equivalent value of the standard deviation of the sampling distribution of the sample means in comparison to the standard deviation in a finite population?

a)

b)

52.

In the formula shown above, what does N stands for?

a)

sample size

b)

population size

c)

number of respondents

d)

number 30

53.

What have you observed with the histogram of the sampling distribution of the sample mean?

a)

The histogram is skewed to the left, regardless of the shape of the population.

b)

It will tend to have an abnormal distribution, regardless of the shape of the population.

c)

The bar in the histogram will be equally distributed

d)

It will tend to have a normal distribution, regardless of the shape of the population.

54.

According to the Central Limit Theorem, For a sample to be large enough, the sample size should be ______.

a)

half of the population

b)

75% of the population size

c)

at least 30

d)

at most 100

55.

Which of the following symbol describes the population mean?

a)

$\mu$

b)

$n$

c)

$x̄$

d)

$σ$

56.

Which of the following symbol describes the population standard deviation?

a)

$\mu$

b)

$s$

c)

$x̄$

d)

$σ$

57.

Consider a population with $\mu=50$ and $\sigma=5$ is taken. Find the mean of the sampling distribution of the sample mean with a sample size of 30.

a)

50

b)

25

c)

20

d)

5

58.

Consider a population with $\mu=50$ and $\sigma=5$ is taken. Find the standard deviation of the sampling distribution of the sample mean with a sample size of 30.

a)

5

b)

0.91

c)

0.71

d)

0

59.

The population mean age of the residents in a certain city is 56.12 years with a standard deviation of 15.3 years. A group of 2000 residents from a certain barangay in the city is taken as a sample. If the population of the city 150 000, find the mean of the sampling distribution of the sample mean of the residents’ ages.

a)

150 000

b)

2 000

c)

15.3

d)

56.12

60.

The population mean age of the residents in a certain city is 56.12 years with a standard deviation of 15.3 years. A group of 2000 residents from a certain barangay in the city is taken as a sample. If the population of the city 150 000, find the standard deviation of the sampling distribution of the sample mean of the residents’ ages.

a)

150 000

b)

0.34

c)

0.5

d)

56.12

61.

These symbols represent the mean and standard deviation for which of the following distributions?

a)

The Population

b)

The Sample

c)

The Sampling Distribution

d)

The Parameter

62.

True or False:

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

a)

True

b)

False

63.

True or False:

As the sample size n increases without limit, the shape of the distribution becomes less normal.

a)

True

b)

False

64.

True or False:

Whatever is the distribution of the population if sample size is increased, the distribution will become approximately normal.

a)

True

b)

False

65.

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

a)

It becomes narrower and bimodal.

b)

It becomes narrower and more normal.

c)

It becomes wider and skewed right.

d)

It becomes wider and more normal.

66.

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?

a)

400

b)

40

c)

25

d)

8

67.

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?

a)

400

b)

40

c)

25

d)

8

68.

REVIEW!

Find the area of the shaded region if the z-score is -0.3

a)

0.6179

b)

0.488

c)

0.3783

d)

0.3821

69.

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

70.

Suppose the teenagers that attend public high schools get an average of 5.7 hours of sleep each night with a standard deviation of 1.7 hours. What is the probability that a randomly selected group of 35 high school students get more than 6 hours of sleep each night?

a)

.430

b)

.148

c)

.281

d)

.087

71.

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

a)

It becomes narrower and bimodal.

b)

It becomes narrower and more normal.

c)

It becomes wider and skewed right.

d)

It becomes wider and more normal.

72.

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?

a)

400

b)

40

c)

25

d)

8

73.

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?

a)

400

b)

40

c)

25

d)

8

74.

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

75.

These symbols represent the mean and standard deviation for which of the following distributions?

a)

The Population

b)

The Sample

c)

The Sampling Distribution

76.

These symbols represent the mean and standard deviation for which of the following distributions?

a)

The Population

b)

The Sample

c)

The Sampling Distribution

77.

What is the standard deviation of the distribution?

a)

1010

b)

20

c)

60

d)

√20

78.

The mean and standard deviation of a population are 200 and 20, respectively.
What is the probability of selecting 25 data values with a mean less than 190?

a)

69%

b)

0.6%

c)

31%

d)

99%

sampling distribution and central limit theorem

Total questions: 78

Worksheet time: 7hrs 28mins

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