AnswersAlgebra II B 2025Unit Test

Unit Test — Unit test Answers

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1
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Destiny performs a hypothesis test on a population with µ = 115 and . Her sample size is 25 with a mean of 120.4. Which of the following correctly depicts the z-statistic for this data?

Question illustration
A
0.04
B
0.90
C
3.53
D
3.93
2
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A local weather enthusiast wants to see if the last five summers have been warmer than normal for Eloy, Arizona. From the National Oceanic and Atmospheric Administration (NOAA), he knows the 30-year average for July was 90° with a standard deviation of 2.1°. The last five summers recorded have an average of 93.5°. If he uses a = 5%, which of the following would be valid based on the data he has gathered?

A
He can conclude that the summers have been warmer than the 30-year average.
B
He can conclude that the summers will continue to be warmer for the next 10 years.
C
He does not have enough information to make a decision.
D
The average for the last five years fits with the 30-year average.
3

The graph below shows three different normal distributions.Which statement must be true?

Question illustration
A
Each distribution has the same mean and the same standard deviation.
B
Each distribution has the same mean and a different standard deviation.
C
Each distribution has a different mean and the same standard deviation.
D
Each distribution has a different mean and a different standard deviation.
4

A simple random sample of size n is drawn from a normally distributed population, and the mean of the sample is , while the standard deviation is s. What is the 99% confidence interval for the population mean? Use the table below to help you answer the question.Confidence Level90%95%99%z*-score1.6451.962.58

Question illustration
A
x Overbar plus-or-minus StartFraction 0.90 times s Over StartRoot n EndRoot EndFraction
Option A
B
x Overbar plus-or-minus StartFraction 0.99 times s Over StartRoot n EndRoot EndFraction
Option B
C
x Overbar plus-or-minus StartFraction 1.645 times s Over StartRoot n EndRoot EndFraction
Option C
D
x Overbar plus-or-minus StartFraction 2.58 times s Over StartRoot n EndRoot EndFraction
Option D
5

When making a statistical inference about the mean of a normally distributed population based on a sample drawn from that population, which of the following statements is correct, all else being equal?

A
The 68% confidence interval is wider than the 90% confidence interval.
B
The 90% confidence interval is narrower than the 95% confidence interval.
C
The 90% confidence interval is wider than the 99% confidence interval.
D
The 99% confidence interval is narrower than the 68% confidence interval.
6

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.
7

A manager records the number of hours, X, each employee works on his or her shift and develops the probability distribution below. Fifty people work for the manager. How many people work 4 hours per shift?Probability DistributionHours Worked: XProbability: P(X)30.14?50.1460.370.3680.06

A
0
B
1
C
2
D
4
8

To conduct a survey about the type of phone service most people in Greenville prefer, 10 different blocks in the neighborhood are chosen. On these 10 blocks, 10 houses are selected at random, and then each resident of each of those houses is interviewed. This type of sampling method is

A
simple random sampling.
B
stratified sampling.
C
systematic random sampling.
D
cluster sampling.
9

The mean test scores with standard deviations of four English classes are given below.ClassMeanStandard DeviationMrs. Jones891.9Mrs. Rijo821.4Mr. Phan733.4Mrs. Scott906.1Which statement is most likely to be true?

A
The scores of Mrs. Scott’s class are the closest to the class mean.
B
The scores of Mr. Phan’s class are the closest to the class mean.
C
The scores of Mrs. Jones’s class are the closest to the class mean.
D
The scores of Mrs. Rijo’s class are the closest to the class mean.
10

Stan guessed on all 10 questions of a multiple-choice quiz. Each question has 4 answer choices. What is the probability that he got at least 2 questions correct? Round the answer to the nearest thousandth.

Question illustration
A
0.211
B
0.244
C
0.756
D
0.944
11

Dwayne and Alisha both correctly graphed a standard normal curve. Which of the following statements is true?

A
Neither the means nor the standard deviations of Dwayne’s and Alisha’s graphs must be the same.
B
The means of Dwayne’s and Alisha’s graphs must be the same but not the standard deviations.
C
The standard deviations of Dwayne’s and Alisha’s graphs must be the same but not the means.
D
Both the means and the standard deviations of Dwayne’s and Alisha’s graphs must be the same.
12

Which normal distribution has the greatest standard deviation?

A
A normal distribution is shown. The curve peaks at 96 and hits the axis at 75 and 115.
Option A
B
A normal distribution is shown. The curve peaks at 60 and hits the axis at 48 and 72.
Option B
C
A normal distribution is shown. The curve peaks at 16 and there is area under the curve at all points.
Option C
D
A normal distribution is shown. The curve peaks at 32 and hits the axis at 28 and 38.
Option D
13

Glenda checks the computer monitors made at her company for defects. It has been shown that 0.5% of the monitors are defective. She decides to check several monitors and record if they are defective. Which of the following will make this process into a binomial experiment?

A
Glenda checks the monitors until she has 300 defective monitors.
B
Glenda checks 300 monitors and records the number that are defective until she gets greater than 0.5% defective monitors.
C
Glenda checks the monitors until she has 300 non-defective monitors.
D
Glenda chooses to check 300 monitors.
17

The hourly wages earned by 20 employees are shown in the first box-and-whisker plot below. The person earning $15 per hour quits and is replaced with a person earning $8 per hour. The graph of the resulting salaries is shown in plot 2.Plot 1 Plot 2 How does the mean and median change from plot 1 to plot 2?

Question illustration
A
The mean and median remain the same.
B
The mean decreases, and the median remains the same.
C
The mean remains the same, and the median decreases.
D
The mean and median decrease.
19

In Juneau, Alaska, the 30-year annual snowfall average is 86.7 inches with a standard deviation of 40.4 inches. The last four years saw an average annual snowfall of 115.7 inches, 62.9 inches, 168.5 inches, and 135.7 inches. Hia performs a hypothesis test on this data to determine if the next 30-year norm will have a different average if the trend from the last four years continues. She uses a significance level of 5%. Which of the following is a conclusion that she may make?

A
The z-statistic is 1.44, so the null hypothesis cannot be rejected.
B
The z-statistic is 1.68, so the null hypothesis cannot be rejected.
C
The z-statistic is 1.85, so the null hypothesis should be rejected.
D
The z-statistic is 4.6, so the null hypothesis should be rejected.
20

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
22

The stem-and-leaf plot below shows the number of pages each student in a class read the previous evening.Which statement is true about the data set?

Question illustration
A
Its median is greater than its mode.
B
It has a range of 52 pages.
C
The value of the first quartile is 13.
D
The data is symmetric.
23

When finding the margin of error for the mean of a normally distributed population from a sample, what is the critical probability, assuming a confidence level of 58%?

A
0.21
B
0.42
C
0.58
D
0.79
25

The lengths of a particular snake are approximately normally distributed with a given mean = 15 in. and standard deviation = 0.8 in. What percentage of the snakes are longer than 16.6 in.?

Question illustration
A
0.3%
B
2.5%
C
3.5%
D
5%

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