Download DM Chapter 16 Test Review

Discrete Math
Chapter 16 Test Review
Name _________________________________
Period ______________
1. The graph to the right represents a population with a normal
distribution.
a. Find the mean and standard deviation of the population.
σ = ___________
µ = ___________
2.43 mm
b. Approximate the five-number summary for the population.
Min = ________
Q1 = ________
M = ________
Q3 = ________
2.57 mm
Max = ________
c. What percent of the population is less than 2.36 mm? __________
d. Suppose the size of the population is N = 530. Approximately how many observations are there
between 2.43 mm and 2.64 mm? __________
2. Find the z-value for a given data point X in a normal distribution of data with mean μ = 37.2 cm
and standard deviation σ = 2.8 cm (round your answers to three decimal places).
a.
X = 31.6
z = __________
b.
X = 38.0
z = __________
3. Find the data point X that corresponds to the given z-value in a normal distribution of data with
μ = 88.4 ºF and standard deviation σ = 2.9 ºF (round your answers to the nearest tenth).
a.
z = –2.667
X = __________
b.
z = 1.025
X = __________
4. In a normal distribution, the data value X1 = 320 has the standardized value z1 = –2 and the data
the data value X2 = 595 has the standardized value z2 = 0.5. Find the mean and standard deviation.
µ = ___________
σ = ___________
5. The graph to the right represents a population with a normal
distribution
a. Find the mean and the standard deviation of the population.
μ = __________
σ = __________
–2.5 ºC
b. Approximate the five-number summary for the population.
Min = ________
Q1 = ________
M = ________
Q3 = ________
2.5 ºC
Max = ________
c. What percent of the population is greater than X = –4.0ºC? ________
d. Suppose the size of the population is N = 117. Approximately how many data values are there
between 2.5 ºC and 4.0 ºC? __________
6. In the 2006-07 school year, 116,209 students took the North Carolina Algebra 1 End-of-Course
(EOC) Test. These students had a mean score of 150.9 with a standard deviation of 10.2. Assume a
normal distribution for their scores.
a. Students who scored between 148 and 157 achieved Level III proficiency.
What percentage of students achieved Level III proficiency?
______________
b. Approximately how many students achieved Level III proficiency?
______________
c. Students who scored below 148 were not considered proficient. What
percentage of students were not proficient?
______________
d. What is the percentile of someone who scored 148?
______________
e. Approximately how many students were not proficient?
______________
f. Students who scored 158 or above achieved Level IV proficiency.
What percentage of students achieved Level IV proficiency?
______________
g. What is the percentile of someone who scored a 158?
______________
h. Approximately how many students scored 158 or above?
______________
7. A research lab took the pulse rate of 50 adult females and found the mean pulse rate to be 79.1
beats per minute with a standard deviation of 7.5 beats per minute. Assuming pulse rates have a
normal distribution.
a. Find the 95% confidence interval for the true mean pulse rate.
__________________________
b. Write a statement about this confidence interval.
c. Suppose the researchers want to estimate the mean within 1 beat per minute. How large must the
sample size be?
n = ___________
8. The optimum diameter for a CD is 12.0 cm. A company that manufactures CDs will ship CD’s
only if they are 99.7% confident that the diameters are between 11.988 and 12.012 cm. Engineers
at the company sample 36 CDs every week to ensure the CD diameters remain within tolerance.
a. What is the acceptable margin of error for the diameter of CDs?
ME = _______________
b. Suppose the engineers take a sample from the production line and find the mean diameter to be
12.0 cm with a standard deviation of 0.036 cm. Based on this sample, what percentage of the CD’s
produced is acceptable?
______________
c. To reach the 99.7% acceptability rate, what should the target standard deviation be?
s = ___________
9. You work for a consumer advocate agency and want to find the mean repair cost of a washing
machine. As part of your study, you randomly select 40 repair costs and find the mean to be
$100.00. From past studies, you assume that the σ is $17.50.
a. Construct a 90% confidence interval for mean repair cost. ______________________________
b. Write a statement about this confidence interval.
c. Determine the minimum required sample size if you want to be 95% confident that the
sample mean is within $10 of the population mean.
n = ___________
10. A college dean conducted a survey and found the 95% confidence interval for the mean GPA of
all students to be 2.86 to 2.98. What was the sample size of her survey? Past surveys have shown a
standard deviation of 0.31.
n = ___________
11. In a survey of 240 corporations, 65 said that if given a choice between hiring a smoker and an
equally qualified non-smoker, they would choose the non-smoker.
a. Find the margin of error for a 95% confidence level. _______________
b. Find a 95% confidence interval for the proportion of corporations who would hire a non-smoker
over a smoker.
________________________________
c. Write a statement about this confidence interval.
12. A company produces sterile disposable gloves for hospitals and wants to determine the
effectiveness of their packaging in keeping the gloves sterile. Previous samples have found that
7.5% of the gloves failed sterility tests.
a. How large a sample do they need if they want to estimate the true population proportion that
failed within 5% with 99% confidence?
n = ___________
b. What would the margin of error be with this sample size if they only required 95% confidence?
ME = _______________
13. Suppose President Obama’s staff decided to conduct a survey to determine popular support for
sending ground troops to Iraq.
a. How large a sample would the pollsters need to estimate the proportion within 3% with 95%
confidence (Hint: Since you don’t have information on proportions, first determine what
proportions would require the largest sample and assume these proportions to answer this question)?
n = ___________
b. How large a sample would the pollsters need to estimate the proportion within 1% with 95%
confidence?
n = ___________
c. How large a sample would the pollsters need to estimate the proportion within 3% with 99%
confidence?
n = ___________
d. Suppose the pollsters used the sample size and confidence level in part 12a above and found the
proportion who supported sending ground troops to Iraq is 27%. Construct a confidence interval for
this proportion.
________________________________
e. If the pollsters had known the true population proportion of those who supported sending ground
troops to Iraq to be 27%, what sample size could they have used?
n = ___________