AnswersAA - F26 Advanced AlgebraApplications with Standard Normal Distribution

Applications with Standard Normal Distribution — Unit test Answers

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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
2
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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.
3

The human resources manager at a company records the length, in hours, of one shift at work, X. He creates the probability distribution below. What is the probability that a worker chosen at random works at least 8 hours?

Question illustration
A
0.62
B
0.78
C
0.84
D
0.96
4

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.
5

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.
6

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
7

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.
8

The graph below is used by company 2 to show the average monthly electric cost based on the electricity provider.How could the graph be redrawn so that the difference in monthly electric cost does not appear as great?

Question illustration
A
The scale on the y-axis could be changed to 0–150.
B
The scale on the y-axis could be changed to 100–120.
C
The interval on the y-axis could be changed to count by 1s.
D
The interval on the y-axis could be changed to count by 20s.
9

Two students have devised a dice game named “Sums” for their statistics class. The game consists of choosing to play odds or evens. Probabilities for “Sums”Roll23456789101112P(roll)Each person takes turns rolling two dice. If the sum is odd, the person playing odds gets points equal to the sum of the roll. If the sum is even, the person playing evens gets points equal to the sum of the roll. Note that the points earned is independent of who is rolling the dice.If Jessica is challenged to a game of Sums, which statement below is accurate in every aspect in guiding her to the correct choice of choosing to play odds or evens?

Question illustration
A
E(evens) will be more because there are more even numbers that result from rolling two dice. Therefore, Jessica should play evens.
B
E(odds) will be more because the probability for each odd number being rolled is greater. Therefore, Jessica should play odds.
C
E(evens) will be more because the value of the even numbers on the dice are more. Therefore, Jessica should play evens.
D
E(evens) = E(odds) because the different probabilities and values end up balancing out, creating a fair game. Therefore, Jessica may choose whichever she likes.
10

The mean of a set of credit scores is and . Which statement must be true about z694?

Question illustration
A
z694 is within 1 standard deviation of the mean.
B
z694 is between 1 and 2 standard deviations of the mean.
C
z694 is between 2 and 3 standard deviations of the mean.
D
z694 is more than 3 standard deviations of the mean.
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

According to a poll, 56% of voters support funding a new community center. A surveyor randomly selects 75 voters and asks each voter if he or she is in favor of the center. If being in favor of the center is a success, what is the probability of a success for this binomial experiment?

A
0.34
B
0.44
C
0.56
D
0.75
13

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
14

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
15

You pick a card at random from an ordinary deck of 52 cards. If the card is a diamond, you get some points; if not, you lose 2 points. What value for the diamonds would make the game fair?

A
12
B
6
C
24
D
3
16

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.
17

For a standard normal distribution, which of the following expressions must always be equal to 1?

A
P (z less-than-or-equal-to a) minus P (negative a less-than-or-equal-to z less-than-or-equal-to z) minus P (z greater-than-or-equal-to a)
Option A
B
P (z less-than-or-equal-to a) minus P (negative a less-than-or-equal-to z less-than-or-equal-to z) + P (z greater-than-or-equal-to a)
Option B
C
P (z less-than-or-equal-to a) + P (negative a less-than-or-equal-to z less-than-or-equal-to z) minus P (z greater-than-or-equal-to a)
Option C
D
P (z less-than-or-equal-to a) + P (negative a less-than-or-equal-to z less-than-or-equal-to z) + P (z greater-than-or-equal-to a)
Option D
18

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.
19

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.
20

A convenience sample differs from a voluntary sample in that

A
a convenience sample is structured based on accessibility to the researcher, and a voluntary sample is based on participant interest.
B
convenience samples survey each participant once, and voluntary samples survey each participant numerous times.
C
convenience sampling is a method of random sampling, and a voluntary sample is not.
D
convenience sampling is not a probability-based method, and voluntary sampling is.

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