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Approximately Normal Distributions of Sample Means

Total questions: 25

Worksheet time: 6hrs 15mins

Name
Class
Date
1.

The Central Limit Theorem states that if a population is (approximately) normal OR the sample size is greater than or equal to ____, then the associated sampling distribution is approximately normal.

a)

30

b)

20

c)

500

d)

80

2.
You need to use the Finite Correction Factor when the sample size is more than ______ of the population size, and you are selecting without replacement.
a)
5%
b)
1%
c)
15%
d)
2%
3.
Which of the following gives the standard deviation of a sampling distribution?
a)
σ/√n
b)
σ/n
c)
σ/(n-1)
d)
σ/[ (√n)-1 ]
4.
Which of the following is the formula for the Finite Correction Factor?
a)
√[ (N-n)/(N-1) ]
b)
√[ (N-1)/(N-n) ]
c)
√[ (n-1)/(N-n) ]
d)
√[ (N-n)/(n-1) ]
5.
Another name for the standard deviation of a sampling distribution is the _______
a)
standard error
b)
variance
c)
sum of squares
d)
expected value
6.
According to de Moivre's Equation, in order to get an estimate that is three times more accurate than your old one, you need to collect _____ times as much data
a)
9
b)
3
c)
6
d)
27
7.
Which sample size for a sampling distribution will have the smallest standard deviation?
a)
n = 10
b)
n = 200
c)
n = 400
d)
n = 1000
8.
For which scenario is it not permissible to use the normal distribution to approximate the sampling distribution?
a)
"x" is Poisson, n =20
b)
"x" is Poisson, n=50
c)
"x" is Normal, n=20
d)
"x" is Normal, n=50
9.
If za is "off the charts" negative, then P(x̄<a) is _____
a)
Approximately 0
b)
Approximately 1
c)
Approximately 0.5
d)
Impossible to calculate
10.
If za is "off the charts" positive, then P(x̄<a) is _____
a)
Approximately 0
b)
Approximately 1
c)
Approximately 0.5
d)
Impossible to calculate
11.
The weight distribution of Unicorns is approximately normal with a mean of 1,000 lbs. and a standard deviation of 25 lbs. In a group of 20 randomly selected unicorns, what is the standard deviation of the sampling distribution ("sigma of x bar")? 
a)
25
b)
1.25
c)
5.59
d)
4
12.
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
13.
The mean and standard deviation of a population are 400 and 40, respectively. Sample size is 25. 
What is the standard deviation of the sampling distribution?
a)
400
b)
40
c)
25
d)
8
14.

The weight distribution of a certain animal is approximately normal with a mean of 1,000 lbs. and a standard deviation of 25 lbs. What is the probability that the mean weight of 25 of these animals selected at random and with replacement is greater than 1,010 pounds?

a)

65.54%

b)

97.72%

c)

2.28%

d)

34.46%

e)

Unknown - we can't assume the shape of the sampling distribution

15.

The mean and standard deviation of a population are 200 and 20, respectively.

If 25 data points are selected from this population at random and with replacement, what is the probability that they have a sample mean of less than 190?

a)

69%

b)

0.6%

c)

31%

d)

99%

e)

Unknown - we can't assume the shape of the sampling distribution

16.

The weights of horses are approximately normal with a mean of 1,500 lbs. and a standard deviation of 30 lbs. What is the probability that the mean weight of 36 randomly selected horses is greater than 1560 pounds?


[Hint: 36 isn't even close to 5% of all the horses in the world.]

a)

65.54%

b)

97.72%

c)

~0%

d)

34.46%

e)

Unknown - we can't assume the shape of the sampling distribution

17.

Increasing the sample size of an opinion poll will reduce the...

a)

bias of the estimates made from the data collected in the poll.

b)

variability of the estimates made from the data collected in the poll.

c)

variability of opinions in the sample.

d)

variability of opinions in the population.

18.
The mean and standard deviation of a (large) population are 200 and 20, respectively. 
If 64 data points are selected at random from this population, what is the probability that the mean value of these data points will be between 195 and 200?
a)
41%%
b)
48%
c)
1.5%
d)
0.5%
19.
The mean and standard deviation of a (large) population are 200 and 20, respectively. 
If 100 data points are selected at random from this population, what is the probability that the mean of this sample will be greater than 202?
a)
45%
b)
36%
c)
25%
d)
16%
20.

A classroom has 30 students. The mean height of students in this classroom is 63 in. with a standard deviation of 4.6 in. Assume these heights approximate a normal distribution.

If ten students are selected at random and without replacement from this classroom, what is the probability that the mean height of the selected students will be less than 62 in.?

a)

0.2033

b)

0.2451

c)

0.1170

d)

0.2420

21.
An elevator has a maximum safe weight capacity of 3,000 lbs. The weights of the people who might use this elevator are approximately normal with μ=190 lbs. and σ=20 lbs.
If fifteen people enter this elevator, what is the probability that the maximum safe weight is exceeded?
a)
2.62%
b)
97.38%
c)
30.85%
d)
69.15%
22.

In which situation would the Finite Correction Factor be needed?

a)

n=40, N=200, selecting with replacement

b)

n=40, N=200, selecting without replacement

c)

n=40, N=2,000, selecting with replacement

d)

n=40, N=2,000, selecting without replacement

23.
Review: In a factory, the weight of the concrete poured into a mold by a machine follows a normal distribution with a mean of 1150 pounds and a standard deviation of 22 pounds. Approximately 95% of molds filled by this machine will hold weights in what interval? 
a)
1084 to 1216 pounds 
b)
1107 to 1150 pounds 
c)
1107 to 1193 pounds 
d)
1128 to 1172 pounds
24.
Review:
Describe the distribution of the data set represented by this histogram.
a)
Left Skewed
b)
Symmetric, but not Uniform
c)
Right Skewed
d)
Uniform
25.

The weights of weightlifters are approximately normal in distribution with a mean of 340 lbs. and a standard deviation of 35 lbs.


Given this, which of the following is more likely?

a)

A randomly-chosen weightlifter will weigh less than 350 lbs.

b)

The mean weight of 30 randomly-chosen weightlifters will be less than 350 lbs.

c)

Both are equally likely

d)

Not enough information to tell.

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