Answers EAP-Algebra Functions and Data Analysis BUnit Test

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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

24%

59%

91%

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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

x Overbar plus-or-minus StartFraction 0.90 times s Over StartRoot n EndRoot EndFraction

x Overbar plus-or-minus StartFraction 0.99 times s Over StartRoot n EndRoot EndFraction

x Overbar plus-or-minus StartFraction 1.645 times s Over StartRoot n EndRoot EndFraction

x Overbar plus-or-minus StartFraction 2.58 times s Over StartRoot n EndRoot EndFraction

Which normal distribution has the greatest standard deviation?

A normal distribution is shown. The curve peaks at 96 and hits the axis at 75 and 115.

A normal distribution is shown. The curve peaks at 60 and hits the axis at 48 and 72.

A normal distribution is shown. The curve peaks at 16 and there is area under the curve at all points.

A normal distribution is shown. The curve peaks at 32 and hits the axis at 28 and 38.

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?

–5

–3.5

–1.5

1.5

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?

Emi failed to find the difference of 89 - 78 correctly.

Emi divided by N - 1 instead of N.

Emi evaluated (46 - 78)2 as -(32)2.

Emi forgot to take the square root of -135.6.

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

z694 is within 1 standard deviation of the mean.

z694 is between 1 and 2 standard deviations of the mean.

z694 is between 2 and 3 standard deviations of the mean.

z694 is more than 3 standard deviations of the mean.

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 .

0.66

1.10

1.31

1.73

Which of the following is a valid probability distribution?

Probability distribution A is shown. The probabilities of 1, 2, 3, 4, 5 and 6 are all 0.2.

Probability distribution B is shown. The probability of 1 is 0.1; 2 is 0.2; 3 is 0.3; 4 is 0.3; 5 is 0.2; 6 is 0.1.

Probability distribution C is shown. The probability of 1 is 0.1; 2 is 0.2; 3 is 0.4; 5 is 0.1; 6 is 0.1.

Probability distribution D is shown. The probability of 1 is 0.2; 2 is 0.1; 3 is 0.1; 4 is 0.5; 5 is 0.1.

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

Neither the means nor the standard deviations of Dwayne’s and Alisha’s graphs must be the same.

The means of Dwayne’s and Alisha’s graphs must be the same but not the standard deviations.

The standard deviations of Dwayne’s and Alisha’s graphs must be the same but not the means.

Both the means and the standard deviations of Dwayne’s and Alisha’s graphs must be the same.

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 probability distribution is shown. The probability of 1 is 0.16; 2 is 0.22; 3 is 0.28; 4 is 0.33.

A probability distribution is shown. The probability of 1 is 0.1; 2 is 0.2; 3 is 0.3; 4 is 0.4.

A probability distribution is shown. The probability of 1 is 0.65; 2 is 0.1; 3 is 0.12; 4 is 0.13.

A probability distribution is shown. The probability of 1 is 0.15; 2 is 0.2; 3 is 0.25; 4 is 0.3.

In a certain normal distribution of scores, the mean is 30 and the standard deviation is 3. Find the z-score corresponding to a score of 23.a.10.00c.7.7b.2.33d.–2.33

Daytime high temperatures in New York in February are normally distributed with an average of 30.2º and a standard deviation of 8.5º.Estimate the probability that the temperature on a given day in February is 39º or higher.a.0.23c.0.815b.0.48d.0.16

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%?

0.21

0.42

0.58

0.79

Six students took a national standardized test for which the average score was 700 and the standard deviation was 150. If a student’s z-value is 1.75 on the test, what was the student’s score?a.850c.921b.875d.963

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?

The game scores of season 2006 have a greater spread than the game scores of season 2008.

The game scores of season 2007 have a greater spread than the game scores of season 2005.

The game scores of season 2006 have a greater spread than the game scores of season 2005.

The game scores of season 2005 have a greater spread than the game scores of season 2006.

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?

0.62

0.78

0.84

0.96

For a standard normal distribution, find the approximate value of . Use the portion of the standard normal table below to help answer the question.zProbability0.000.50000.160.56360.220.58710.780.78231.000.84131.160.87701.780.96252.000.9772

22%

66%

78%

88%

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

Each distribution has the same mean and the same standard deviation.

Each distribution has the same mean and a different standard deviation.

Each distribution has a different mean and the same standard deviation.

Each distribution has a different mean and a different standard deviation.

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?

The scores of Mrs. Scott’s class are the closest to the class mean.

The scores of Mr. Phan’s class are the closest to the class mean.

The scores of Mrs. Jones’s class are the closest to the class mean.

The scores of Mrs. Rijo’s class are the closest to the class mean.

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?

The 68% confidence interval is wider than the 90% confidence interval.

The 90% confidence interval is narrower than the 95% confidence interval.

The 90% confidence interval is wider than the 99% confidence interval.

The 99% confidence interval is narrower than the 68% confidence interval.

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.?

0.3%

2.5%

3.5%

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

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)

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)

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)

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)

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

The lengths of a lawn mower part are approximately normally distributed with a given mean = 4 in. and standard deviation = 0.2 in. What percentage of the parts will have lengths between 3.8 in. and 4.2 in.?

34%

68%

95%

99.7%

The graph below shows the average daily temperatures on January 1 from 1900 to 1934 for city A.The mean of the temperatures in the chart is 24° with standard deviation of 4°. How many years had temperatures within one standard deviation of the mean?

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