Free Printable 2nd Summative Test in Research 9 (The Central Limit Theorem)

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2nd Summative Test in Research 9 (The Central Limit Theorem)

Total questions: 30

Worksheet time: 5hrs 5mins

Name

Class

Date

Which of the following statements is correct?

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

The mean of the sampling distribution of the sample means is less than the population mean.

The means of the samples drawn from a population are always equal to the population mean.

The means of the samples drawn from a population may be equal greater than or less than the population mean.

How many possible of size n=3 can be drawn from a population of size 12?

1728

144

220

What is the shape of the sampling distribution of the means if random samples of size n become larger?

Left skewed

Right skewed

Normal

Rectangular

A certain population has a mean of 15.4 and a standard deviation of 5.6. If random samples of size 5 is taken from this population, which of the following statements is correct?

The mean of the sampling distribution of the sample means is equal to 15.4.

The mean of the sampling distribution of the sample means is less than 15.4.

The standard deviation of the sampling distribution of the sample means is 5.6.

The standard deviation of the sampling distribution of the sample means is 15.4.

Which sample size will give a smaller standard error of the mean?

The average precipitation for the first 7 months of the year is 19.32 inches with a standard deviation of 2.4 inches. Assume that the average precipitation is normally distributed.

What is the probability that a randomly selected year will have precipitation greater than 18 inches for the first 7 months?

19.32 inches

22.4 inches

20.52 inches

15.56 inches

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

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

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

The Population

The Sample

The Sampling Distribution

10.

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

11.

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

12.

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?

.430

.148

.281

.087

13.

True or False:

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

True

False

14.

True or False:

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

True

False

15.

True or False:

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

True

False

16.

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

17.

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

18.

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

19.

What shape is a normal distribution curve?

Half curve

Round curve

Bell curve

Square curve

20.

According to the empirical rule, what percentage of data falls within 1 standard deviation?

25%

68%

95%

99.7%

21.

According to the empirical rule, how much of the data falls within 3 standard deviations?

25%

68%

95%

99.7%

22.

The mean number of accidents a week at a company is 6.4 with a standard deviation of 1.5. What proportion of weeks would you expect to have less than 5 accidents?

0.6915

0.1762

0.8238

-0.93

23.

The average waist size for teenage males is 29 inches with a standard deviation of 1.4 inch. If waist sizes are normally distributed, estimate the proportion of teenagers who will have waist sizes greater than 31 inches?

92.4%

10.5%

16%

7.6%

24.

The mean number of accidents a week at a company is 6.4 with a standard deviation of 1.5. What proportion of weeks would you expect to have more than 7 accidents?

0.3446

0.2856

0.4

0.6554

25.

The mean GPA of students in a course at UCDavis is 3.2 with a standard deviation of 0.3. What percent of students in the course have a GPA between 2.9 and 3.8?

81.5%

47.5%

68%

95%

26.

Between what two standard deviations of a normal distribution contain 68% of the data?

one below and one above

two below and two above

two below and zero

zero and two above

27.

The shelf life of a particular dairy product is normally distributed with a mean of 12 days and a standard deviation of 3 days.

About what percent of the products last between 12 and 15 days?

68%

34%

16%

2.5%

28.

Which sample size for a sampling distribution will have the SMALLEST standard deviation?

n = 10

n = 200

n = 400

n = 1000

29.

A soft drink bottler claims that, on average, cans contain 12 oz. of soda. Suppose the true distribution of soda volumes is normally distributed with a mean of 12 oz. and a standard deviation of .16 oz. Sixteen cans are randomly selected and their volumes are measured. What is the probability the average volume will be between 11.96 and 12.08 oz.?

.2902

.8186

.7424

.3194

30.

Frequent fliers of a particular airline fly a random number of miles each year, having mean and standard deviation (in thousands of miles) of 23 and 11, respectively. The airline decides to randomly select 25 of these fliers and record the number of miles that each individual flew the past year. Compute the approximate probability that the sample mean of the miles flew will be greater than 26 thousand miles.

.3925

.1983

.873

.087

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2nd Summative Test in Research 9 (The Central Limit Theorem)

Total questions: 30

Worksheet time: 5hrs 5mins

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