AnswersAA - F26 Advanced AlgebraApplications with Standard Normal Distribution

Applications with Standard Normal Distribution — Unit test Answers

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The annual salaries of all employees at a financial company are normally distributed with a mean = $34,000 and a standard deviation = $4,000. What is the z-score of a company employee who makes an annual salary of $28,000?

Question illustration
A
–5
B
–3.5
C
–1.5
D
1.5
2
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Alex records the running time—the number of minutes a movie lasts from start to finish—of 50 popular movies. The distribution of times, in minutes, is displayed in the histogram below.

Question illustration
A
uniform
B
skewed left
C
skewed right
D
roughly symmetric
3

A college student would like to investigate the prices of large sandwiches offered near college campuses. Two random samples of 50 shops that sell sandwiches near the campuses of two colleges were taken and the price they charge for a large sandwich was recorded. One sample was taken for shops near City College, and one sample was taken for shops near Main Line University. The results are displayed in the cumulative relative frequency histograms below.Which is a correct comparison of sandwich prices based on the histograms?

Question illustration
A
The interval from $11 to $12 contains the most shops for both college locations.
B
More shops charge between $12 and $13 near Main Line University than City College.
C
The median price lies between $10 to $11 for both City College and Main Line University.
D
Fewer shops sell sandwiches for under $10 near City College than near Main Line University.
4

A restaurant chain would like to measure the proportion of customers who are generally satisfied with the service provided by its staff. At the end of the meal, as the check is delivered to the table, the server asks those at the table to rate their satisfaction with the service provided as "Very Satisfied,” "Satisfied,” or "Not Satisfied.” During a one-week period, 147 customers were surveyed and 135 (93%) reported they were either Satisfied or Very Satisfied. How might the results be biased in obtaining an estimate of all customers who are satisfied with service?

A
Because of response bias, the survey results may overestimate the true proportion of satisfied customers.
B
Because of response bias, the survey results may underestimate the true proportion of satisfied customers.
C
Because of voluntary response bias, the survey results may overestimate the true proportion of satisfied customers.
D
Because customers were surveyed over a one-week period, the results should provide an accurate estimate of satisfied customers.
5

A high school student volunteers to present a report to the administration about the types of lunches students prefer. He surveys members of his class and records their choices. What type of sampling did the student use?

A
systematic random sampling
B
voluntary sampling
C
convenience sampling
D
stratified sampling
6

The resting heart rates for 80 women aged 46–55 in a simple random sample are normally distributed, with a mean of 71 beats per minute and a standard deviation of 6 beats per minute. Assuming a 90% confidence level (90% confidence level = z-score of 1.645), what is the margin of error for the population mean?Remember, the margin of error, ME, can be determined using the formula .

Question illustration
A
0.66
B
1.10
C
1.31
D
1.73
7

The table below shows the ages of houses to the nearest year in a neighborhood. Using the age of the houses as the random variable, X, which graph shows the probability distribution, PX(x), of a randomly chosen house?Age of HouseNumber of Houses115220325430

A
A probability distribution is shown. The probability of 1 is 0.16; 2 is 0.22; 3 is 0.28; 4 is 0.33.
Option A
B
A probability distribution is shown. The probability of 1 is 0.1; 2 is 0.2; 3 is 0.3; 4 is 0.4.
Option B
C
A probability distribution is shown. The probability of 1 is 0.65; 2 is 0.1; 3 is 0.12; 4 is 0.13.
Option C
D
A probability distribution is shown. The probability of 1 is 0.15; 2 is 0.2; 3 is 0.25; 4 is 0.3.
Option D
8

Research suggests that students could benefit from later school starting times. A school administrative team is considering a proposal to move the starting time of the local schools one hour later than the current start time. To measure interest in the proposal, members of the team randomly select subjects attending a large high school soccer tournament played on the high school grounds on a Saturday morning. The team finds that 58% of those surveyed support a later high school start time. Which type of bias is most likely to be present in the survey results?

A
This is undercoverage bias because adults with older children are more likely to be included in the sample.
B
This is question wording bias because the phrasing of the later start times question may be confusing to some subjects.
C
This is nonresponse bias because some of those selected may choose to not provide their opinion on later start times.
D
This is voluntary response bias because vocal supporters of later start times will be more likely to offer their opinion.
9

The stemplot below represents the number of bite-size snacks grabbed by 37 students in an activity for a statistics class.

Question illustration
A
The distribution of the number of snacks grabbed is skewed right with a center around 18 and varies from 15 to 45. There are no outliers.
B
The distribution of the number of snacks grabbed is symmetric with a center around 18 and varies from 12 to 45. There are possible outliers at 38, 42, and 45.
C
The distribution of the number of snacks grabbed is skewed left with a center around 18 and varies from 12 to 45. There are possible outliers at 38, 42, and 45.
D
The distribution of the number of snacks grabbed is skewed right with a center around 18 and varies from 12 to 45. There are possible outliers at 38, 42, and 45.
10

The dotplot below displays 26 students’ scores on a 30-point statistics quiz.

Question illustration
A
The distribution of quiz scores is skewed left with a center around 24 and varies from 12 to 30. There are possible outliers at 12, 14, 15, and 16.
B
The distribution of quiz scores is skewed right with a center around 24 and varies from 12 to 30. There are possible outliers at 12, 14, 15, and 16.
C
The distribution of quiz scores is unimodal symmetric with a center around 24 and varies from 12 to 30. There are possible outliers at 12, 14, 15, and 16.
D
The distribution of quiz scores is unimodal symmetric with a center around 26 and varies from 20 to 30. There are possible outliers at 12, 14, 15, and 16.
11

The mean game scores and standard deviations of four seasons of a football team are given below.SeasonMeanStandard Deviation2005193.52006212.82007121.0200894.0Which statement must be true?

A
The game scores of season 2006 have a greater spread than the game scores of season 2008.
B
The game scores of season 2007 have a greater spread than the game scores of season 2005.
C
The game scores of season 2006 have a greater spread than the game scores of season 2005.
D
The game scores of season 2005 have a greater spread than the game scores of season 2006.
12

The scores of the students on a standardized test are normally distributed, with a mean of 500 and a standard deviation of 110. What is the probability that a randomly selected student has a score between 350 and 550? Use the portion of the standard normal table below to help answer the question.zProbability0.000.50000.250.59870.350.63680.450.67361.000.84131.260.89611.350.91151.360.9131

A
9%
B
24%
C
59%
D
91%
13

The dotplots below display the scores for two classes on a 30-point statistics quiz. Class A has 26 students and Class B has 25 students.Which statement best compares the variability of the quiz scores for Class A and Class B?

Question illustration
A
The scores on the quiz for Class A have more variability than the scores for Class B.
B
The scores on the quiz for Class B have more variability than the scores for Class A.
C
The scores on the quiz for Class A have less variability than the scores for Class B.
D
The scores on the quiz for Class B have about the same variability as the scores for Class A.
14

The stemplot below represents the number of bite-size snacks grabbed by 32 students in an activity for a statistics class.

Question illustration
A
skewed to the left
B
bimodal symmetric
C
skewed to the right
D
unimodal symmetric
15

Emi computes the mean and variance for the population data set 87, 46, 90, 78, and 89. She finds the mean is 78. Her steps for finding the variance are shown below.What is the first error she made in computing the variance?

Question illustration
A
Emi failed to find the difference of 89 - 78 correctly.
B
Emi divided by N - 1 instead of N.
C
Emi evaluated (46 - 78)2 as -(32)2.
D
Emi forgot to take the square root of -135.6.

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