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Central limit theorem for Mean (Averages)- Practice quiz

Total questions: 20

Worksheet time: 1hrs 10mins

Name
Class
Date
1.

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.

2.

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.

3.

Consider a population with μ=50\mu=50  and σ=5\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

4.

Consider a population with μ=50\mu=50  and σ=5\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

5.

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

6.

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

7.
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
8.
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
9.
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
10.
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
11.
What is the standard deviation of the distribution?
a)
1010
b)
20
c)
60
d)
√20
12.
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%
13.
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. 
14.
Recall N(1000, 25). In a group of 20 randomly selected unicorns, what is the standard deviation of the sampling distribution? 
a)
25
b)
1.25
c)
5.59
d)
4
15.
The weights of unicorns are given by N(1000, 25). What is the probability that the average weight of 25 randomly selected unicorns is greater than 1010 pounds? 
a)
65.54%
b)
97.72%
c)
2.28%
d)
34.46%
16.

A customer service department monitors how long their callers wait on hold before being helped. The time spent by the callers on hold follows a normal distribution similar to this:

Suppose that we took random samples of 30 callers and calculated the sample mean time spent on hold for each sample of customers. We can assume that the callers in each sample are independent.

What would be the shape of the sampling distribution of the sample mean?

a)

Skewed to the left

b)

Skewed the right

c)

Approximately normal

d)

Unknown, there is not enough information to determine

17.

Let X be a random variable with mean μ=20 and standard deviation σ=4. A sample of size 64 is randomly selected from this population. What is the approximate probability that the sample mean X\overline{X}   of the selected sample is less than 19?

(give your answer to 4 decimal places)

(a)  

18.

In the first semester of the year 2003, the average return for a group of 251 investing companies was 4.5% and the standard deviation was 1.5%. If a sample of 40 companies is randomly selected from this group, what is the approximate probability that the average return of the companies in this sample was between 4% and 5% in the first semester of the year 2003?

(give your answer to 3 decimal places)

(a)  

19.

A population of 29-year-old males has a mean salary of $29,321 with a standard deviation of $2,120. If a sample of 100 men is taken, what is the probability their mean salaries will be less than $29,000?

give your answer to 2 decimal places

(a)  

20.

In a recent study reported Oct. 29, 2012, on the Flurry Blog, the mean age of tablet users is 34 years. Suppose the standard deviation is 15 years. Take a sample of size n = 100.

Find the 95th percentile for the sample mean age (to one decimal place).

(a)