Exam (elaborations)
Sta1610 Assignment 3 2023
- Institution
- University Of South Africa (Unisa)
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7/29/23, 2:45 PM Assessment 3: Attempt reviewSTA1610-23-Y Welcome Message Assessment 3
QUIZ
Started on Saturday, 29 July 2023, 2:28 PM
State Finished
Completed on Saturday, 29 July 2023, 2:45 PM
Time taken 16 mins 49 secs
Marks 17.00/20.00
Grade 85.00 out of 100.00
Question 1
Correct
Mark 2.00 out of 2.00
Which one of the following statements is incorrect with regard to the normal
probability distribution?
a. The standard normal distribution has a mean of and a standard deviation
of .
b. The area to right of mean of a standard normal distribution is and
the area left of the mean of a standard normal distribution is also .
c. The -score of the mean of a normal probability distribution is .
d. of the values of a normal random variable are within standard
deviation of the mean.
e. The smaller the value of the standard deviation, the narrow and steeper the
curve.
Question 2
Partially correct
Mark 0.50 out of 2.00
Consider a standard normal distribution, . Suppose that the area
between and is i.e., . Determine the value of
and choose the correct answer from the list of options below.
a.
b.
c.
d.
e.
https://mymodules.dtls.unisa.ac.za/mod/quiz/review.php?attempt=11639807&cmid=621492 1/4
,7/29/23, 2:45 PM Assessment 3: Attempt review
Question 3
Correct
Mark 2.00 out of 2.00
A local company manufactures rechargeable lights with mean battery life of
hours and a standard deviation of hours. What is the probability that a randomly
selected rechargeable light will have a battery life of at least hours?
a.
b.
c.
d.
e. 0.9000
Question 4
Partially correct
Mark 1.50 out of 2.00
Consider the information from the previous question. Remember rechargeable lights
have a mean battery life of \( 80 \) hours with a standard deviation of \( 8 \) hours.
Suppose that the local company manufactures the lights for a lighting warehouse.
It is observed that the warehouse rejects about 25% of the lights (because they do
not pass the minimum battery life test).
Determine the minimum battery life accepted by the lighting warehouse.
a. Approximately \( 72 \hspace{1.5mm} \textrm{hours} \)
b. Approximately \( 73 \hspace{1.5mm} \textrm{hours} \)
c. Approximately \( 74 \hspace{1.5mm} \textrm{hours} \)
d. Approximately \( 75 \hspace{1.5mm} \textrm{hours} \)
e. Approximately \( 76 \hspace{1.5mm} \textrm{hours} \)
Question 5
Correct
Mark 2.00 out of 2.00
A random sample of \( n \) observations is selected from a population with a mean
of \( 225 \) and a standard deviation of \( 25 \). Which one of the following
statements regarding the sampling distribution of the mean is incorrect?
a. According to the cental limit theorem, the sampling distribution of the
sample mean \( \bar{X} \) can be approximated by a normal distribution as
the sample size \( n \) becomes large.
b. The mean of the sampling distribution of \( \bar{X} \) is \( 225 \).
c. If the sample size \( n=20 \), then the standard error of the mean is \( 5.59
\).
d. If the sample size \( n=30 \), then the standard error of the mean is \( 4.56
\).
e. If the sample size \( n=40 \), then the standard error of the mean is \(
3.26 \).
https://mymodules.dtls.unisa.ac.za/mod/quiz/review.php?attempt=11639807&cmid=621492 2/4
, 7/29/23, 2:45 PM Assessment 3: Attempt review
Question 6
Correct
Mark 2.00 out of 2.00
In a random sample of size \( 99 \), the sample proportion of interest \( 0.73 \).
Suppose that true population proportion in known and equal to \( 0.80 \). Calculate
the standard error of the proportion and choose the correct answer from the list of
options below.
a. \( 0.0402 \)
b. \( 0.0423 \)
c. \( 0.0016 \)
d. \( 0.0018 \)
e. \( 0.0300 \)
Question 7
Correct
Mark 2.00 out of 2.00
Consider a random variable \( X \) with a population mean of \( 75 \) and a
population standard deviation of \( 10 \) i.e., \( X \sim N (75,10^2) \). Suppose that a
sample of size \( 20 \) is selected from the population, what is the probability that
the sample mean \( \bar{X} \) is between \( 76 \) and \( 80 \)?
a. \( 0.3139 \)
b. \( 0.9875 \)
c. \( 0.6736 \)
d. \( 0.3264 \)
e. \( 0.0125 \)
Question 8
Correct
Mark 2.00 out of 2.00
Consider the random variable \( X \sim N (75,10^2) \) from the previous question.
Now suppose that a sample of size \( 30 \) is selected from the population. There is
a \( 90.99\% \) chance that the sample mean \( \bar{X} \) is less than or equal to the
value \( x \), what is the value of \( x \)?
a. \( 77.45 \)
b. \( 72.55 \)
c. \( 73.47 \)
d. \( 1.34 \)
e. \( -0.84 \)
https://mymodules.dtls.unisa.ac.za/mod/quiz/review.php?attempt=11639807&cmid=621492 3/4
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