MATH 110 MODULE 5: Problem Set: Introduction to
Statistics - Key - 2025B PASSED SOLUTION WITH
FORMULA SHEET Portage Learning
M5: Problem Set
• Due No due date
• Points 5
• Questions 7
• Time Limit None
Instructions
Attempt History
Attempt Time Score
LATEST Attempt 1 834 minutes 5 out of 5
Score for this quiz: 5 out of 5
Submitted Apr 22 at 11:29am This
attempt took 834 minutes.
Question 1
pts
Suppose that 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?
Your Answer:
n/600 .05
n =(.005) (600)
n= 30
In order to use infinite standard deviation formula, we must have:
,So, the sample size must be less than 30.
Question 2
pts
Suppose that you take a sample of size 15 from a population that is known to be normally distributed. Can the
sampling distribution of x̄ be approximated by a normal probability distribution?
Your Answer:
Yes , the sampling distribution of x̄ can be approximated by a normal probability distribution because the
population is normally distributed
Yes, the sampling distribution of x̄ can be approximated by a normal probability distribution because the
population is normally distributed. (Recall that if the population is normally distributed, the sampling
distribution of x̄ can be approximated by a normal probability distribution even for very small sample sizes.)
Question 3
pts
Suppose that you take a sample of size 20 from a population that is not normally distributed. Can the sampling
distribution of x̄ be approximated by a normal probability distribution?
Your Answer:
No, the sampling distribution of x̄ cannot be approximated by a normal probability distribution because the
population is not normally distributed.
No, the sampling distribution of x̄ cannot be approximated by a normal probability distribution in this case.
(Recall that if the population is not normally distributed, the sample size must be at least 30.)
Question 4
pts
Suppose a pharmaceutical company wants to do a study of the commissions of its sales force. Let's assume
that there are 4,300 sales people and the population mean for the sales force is $52,400 in commissions and
has a population standard deviation of $3,500. What is the probability that a simple random sample of 50
members of the sales force will have commissions within $400 of the population mean?
Your Answer:
, We first find the standard deviation of the sample distribution:
= σ/
¯
σ x
= 3500/
= 494.97
¯
x -μ /o ¯
z= x
= 52000 - 52400/494.97
= -.81
Therefore, P(-.81 < Z<.81)
= P(Z<.81) - P(Z < -.81)
= 0.79103 - 0.20897
= .58
We calculate the standard deviation of the sample distribution:
We now have the necessary information needed to determine the probability the sample mean x̄ will be
between $52,000 and $52,800 this is the range which is within $400 of the population mean µ of
$52,400.)
Calculate the z-score:
Using this formula, we will calculate the two z-scores that we will use to answer our question.
Statistics - Key - 2025B PASSED SOLUTION WITH
FORMULA SHEET Portage Learning
M5: Problem Set
• Due No due date
• Points 5
• Questions 7
• Time Limit None
Instructions
Attempt History
Attempt Time Score
LATEST Attempt 1 834 minutes 5 out of 5
Score for this quiz: 5 out of 5
Submitted Apr 22 at 11:29am This
attempt took 834 minutes.
Question 1
pts
Suppose that 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?
Your Answer:
n/600 .05
n =(.005) (600)
n= 30
In order to use infinite standard deviation formula, we must have:
,So, the sample size must be less than 30.
Question 2
pts
Suppose that you take a sample of size 15 from a population that is known to be normally distributed. Can the
sampling distribution of x̄ be approximated by a normal probability distribution?
Your Answer:
Yes , the sampling distribution of x̄ can be approximated by a normal probability distribution because the
population is normally distributed
Yes, the sampling distribution of x̄ can be approximated by a normal probability distribution because the
population is normally distributed. (Recall that if the population is normally distributed, the sampling
distribution of x̄ can be approximated by a normal probability distribution even for very small sample sizes.)
Question 3
pts
Suppose that you take a sample of size 20 from a population that is not normally distributed. Can the sampling
distribution of x̄ be approximated by a normal probability distribution?
Your Answer:
No, the sampling distribution of x̄ cannot be approximated by a normal probability distribution because the
population is not normally distributed.
No, the sampling distribution of x̄ cannot be approximated by a normal probability distribution in this case.
(Recall that if the population is not normally distributed, the sample size must be at least 30.)
Question 4
pts
Suppose a pharmaceutical company wants to do a study of the commissions of its sales force. Let's assume
that there are 4,300 sales people and the population mean for the sales force is $52,400 in commissions and
has a population standard deviation of $3,500. What is the probability that a simple random sample of 50
members of the sales force will have commissions within $400 of the population mean?
Your Answer:
, We first find the standard deviation of the sample distribution:
= σ/
¯
σ x
= 3500/
= 494.97
¯
x -μ /o ¯
z= x
= 52000 - 52400/494.97
= -.81
Therefore, P(-.81 < Z<.81)
= P(Z<.81) - P(Z < -.81)
= 0.79103 - 0.20897
= .58
We calculate the standard deviation of the sample distribution:
We now have the necessary information needed to determine the probability the sample mean x̄ will be
between $52,000 and $52,800 this is the range which is within $400 of the population mean µ of
$52,400.)
Calculate the z-score:
Using this formula, we will calculate the two z-scores that we will use to answer our question.
