,MATH 110 Module 5 | Practice Q&A | 2026/2027 | Statistics | Portage
Learning | 100% PASS
1. The sampling distribution of the sample mean x̄ is defined as:
A) The distribution of all possible sample means from a population
B) The distribution of individual data values in a sample
C) The distribution of the population from which samples are drawn
D) The distribution of sample variances
Correct Answer: The distribution of all possible sample means from a
population
Rationale: The sampling distribution of x̄ is the probability distribution of all
possible values of the sample mean that could be obtained from all possible
samples of a given size n from a population.
2. According to the Central Limit Theorem, for a sufficiently large sample
size, the sampling distribution of x̄ will be approximately normal regardless
of:
A) The sample size
B) The population standard deviation
C) The shape of the population distribution
D) The sample mean
Correct Answer: The shape of the population distribution
Rationale: The Central Limit Theorem states that the sampling distribution of
x̄ becomes approximately normal as sample size increases, regardless of the
shape of the population distribution, provided the sample size is sufficiently
large (typically n ≥ 30).
,3. Suppose you take a sample of size 18 from a population that is not
normally distributed. Can the sampling distribution of x̄ be approximated by
a normal probability distribution?
A) Yes, because the sample size is greater than 15
B) No, because the population is not normally distributed and n < 30
C) Yes, because the Central Limit Theorem always applies
D) No, because the sample size is too large
Correct Answer: No, because the population is not normally distributed and n
< 30
Rationale: When the population is not normally distributed, we need a
sample size of at least 30 to approximate the sampling distribution by a
normal distribution. Since n = 18 < 30, the normal approximation cannot be
used.
4. Suppose you take a sample of size 35 from a population that is not
normally distributed. Can the sampling distribution of x̄ be approximated by
a normal probability distribution?
A) Yes, because n ≥ 30
B) No, because the population is not normally distributed
C) Yes, because the sample size is exactly 35
D) No, because the sample size is too large
Correct Answer: Yes, because n ≥ 30
Rationale: By the Central Limit Theorem, when n ≥ 30, the sampling
distribution of x̄ can be approximated by a normal distribution regardless of
the population distribution. Since n = 35 ≥ 30, the normal approximation is
valid.
, 5. Suppose you are attempting to estimate the annual income of 1100
families. In order to use the infinite standard deviation formula, what sample
size, n, should you use?
A) n = 1100
B) n ≤ 55
C) n ≥ 55
D) n = 100
Correct Answer: n ≤ 55
Rationale: To use the infinite standard deviation formula, the sample size
must be less than or equal to 5% of the population: n/N ≤ 0.05. For N =
1100, n ≤ 0.05 × 1100 = 55.
6. Suppose you are attempting to estimate the weight of 600 parts. In order
to use the infinite standard deviation formula, what sample size, n, should
you use?
A) n = 600
B) n ≤ 30
C) n ≥ 30
D) n = 50
Correct Answer: n ≤ 30
Rationale: To use the infinite standard deviation formula, n/N ≤ 0.05. For N =
600, n ≤ 0.05 × 600 = 30.
Learning | 100% PASS
1. The sampling distribution of the sample mean x̄ is defined as:
A) The distribution of all possible sample means from a population
B) The distribution of individual data values in a sample
C) The distribution of the population from which samples are drawn
D) The distribution of sample variances
Correct Answer: The distribution of all possible sample means from a
population
Rationale: The sampling distribution of x̄ is the probability distribution of all
possible values of the sample mean that could be obtained from all possible
samples of a given size n from a population.
2. According to the Central Limit Theorem, for a sufficiently large sample
size, the sampling distribution of x̄ will be approximately normal regardless
of:
A) The sample size
B) The population standard deviation
C) The shape of the population distribution
D) The sample mean
Correct Answer: The shape of the population distribution
Rationale: The Central Limit Theorem states that the sampling distribution of
x̄ becomes approximately normal as sample size increases, regardless of the
shape of the population distribution, provided the sample size is sufficiently
large (typically n ≥ 30).
,3. Suppose you take a sample of size 18 from a population that is not
normally distributed. Can the sampling distribution of x̄ be approximated by
a normal probability distribution?
A) Yes, because the sample size is greater than 15
B) No, because the population is not normally distributed and n < 30
C) Yes, because the Central Limit Theorem always applies
D) No, because the sample size is too large
Correct Answer: No, because the population is not normally distributed and n
< 30
Rationale: When the population is not normally distributed, we need a
sample size of at least 30 to approximate the sampling distribution by a
normal distribution. Since n = 18 < 30, the normal approximation cannot be
used.
4. Suppose you take a sample of size 35 from a population that is not
normally distributed. Can the sampling distribution of x̄ be approximated by
a normal probability distribution?
A) Yes, because n ≥ 30
B) No, because the population is not normally distributed
C) Yes, because the sample size is exactly 35
D) No, because the sample size is too large
Correct Answer: Yes, because n ≥ 30
Rationale: By the Central Limit Theorem, when n ≥ 30, the sampling
distribution of x̄ can be approximated by a normal distribution regardless of
the population distribution. Since n = 35 ≥ 30, the normal approximation is
valid.
, 5. Suppose you are attempting to estimate the annual income of 1100
families. In order to use the infinite standard deviation formula, what sample
size, n, should you use?
A) n = 1100
B) n ≤ 55
C) n ≥ 55
D) n = 100
Correct Answer: n ≤ 55
Rationale: To use the infinite standard deviation formula, the sample size
must be less than or equal to 5% of the population: n/N ≤ 0.05. For N =
1100, n ≤ 0.05 × 1100 = 55.
6. Suppose you are attempting to estimate the weight of 600 parts. In order
to use the infinite standard deviation formula, what sample size, n, should
you use?
A) n = 600
B) n ≤ 30
C) n ≥ 30
D) n = 50
Correct Answer: n ≤ 30
Rationale: To use the infinite standard deviation formula, n/N ≤ 0.05. For N =
600, n ≤ 0.05 × 600 = 30.
