Question 1

Use the following to answer the questions below:
A student suspects that the length of songs currently on her Spotify playlist are approximately normally distributed with a mean of 257 seconds and standard deviation 62 seconds.
-The longest 25% of songs are longer than what length? Report your answer with one decimal place.

Accepted Answer

To find the length of the longest 25% of songs, we need to find the 75th percentile of a normal distribution with a mean of 257 seconds and a standard deviation of 62 seconds. Using a standard normal distribution table or calculator, the z-score for the 75th percentile is approximately 0.674. Using the formula: length = mean + (z-score * standard deviation), we get: 257 + (0.674 * 62) = 298.8 seconds.

Question 2

Use the following to answer the questions below:
A student suspects that the length of songs currently on her Spotify playlist are approximately normally distributed with a mean of 257 seconds and standard deviation 62 seconds.
-The symmetric middle 90% of songs have lengths between what two values? Round all values to one decimal place.

Accepted Answer

The middle 90% of songs have lengths between 155.0 seconds and 359.0 seconds. This is because the mean is 257 seconds and the standard deviation is 62 seconds, so the z-scores for the 5th and 95th percentiles are -1.645 and 1.645, respectively. Multiplying these z-scores by the standard deviation and adding the mean gives the corresponding lengths.

Question 3

Use the following to answer the questions below:
Robins are common birds in North America. Suppose that the wingspan of robins is approximately normal with mean 14 inches and standard deviation 0.7 inches.
-Draw a sketch of this normal distribution and label at least three points on the horizontal axis.

Accepted Answer

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Question 4

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Robins are common birds in North America. Suppose that the wingspan of robins is approximately normal with mean 14 inches and standard deviation 0.7 inches.
-What proportion of robins have wingspans less than 13 inches? Report your answer with three decimal places.

Accepted Answer

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Question 5

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Robins are common birds in North America. Suppose that the wingspan of robins is approximately normal with mean 14 inches and standard deviation 0.7 inches.
-What proportion of robins have wingspans longer 15.5 inches? Report your answer with three decimal places.

Accepted Answer

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Question 6

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Robins are common birds in North America. Suppose that the wingspan of robins is approximately normal with mean 14 inches and standard deviation 0.7 inches.
-What proportion of robins have wingspans between 12.5 and 13.5 inches? Report your answer with three decimal places.

Accepted Answer

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Question 7

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Robins are common birds in North America. Suppose that the wingspan of robins is approximately normal with mean 14 inches and standard deviation 0.7 inches.
-What is the 30th percentile of robin wingspans? Report your answer with two decimal places.

Accepted Answer

The 30th percentile corresponds to a z-score of approximately -0.524. Using the formula for a normal distribution, X = μ + zσ, where μ = 14 and σ = 0.7, we calculate X = 14 + (-0.524)(0.7) ≈ 13.63 inches.

Question 8

Use the following to answer the questions below:
Robins are common birds in North America. Suppose that the wingspan of robins is approximately normal with mean 14 inches and standard deviation 0.7 inches.
-The largest 20% of robins have wingspans longer than what value? Report your answer with two decimal places.

Accepted Answer

To find the wingspan that separates the largest 20% of robins, we need to find the 80th percentile of a normal distribution with mean 14 and standard deviation 0.7. Using a standard normal distribution table or calculator, the z-score for the 80th percentile is approximately 0.84. Applying the formula: wingspan = mean + (z-score * standard deviation), we get 14 + (0.84 * 0.7) = 14.588, which rounds to 14.59 inches.

Question 9

Use the following to answer the questions below:
Final grades in Professor Albert's large calculus class are approximately normally distributed with a mean of 76 (%) and standard deviation of 8 (%).
-Draw a sketch of this normal distribution and label at least three points on the horizontal axis.

Accepted Answer

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Question 10

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Final grades in Professor Albert's large calculus class are approximately normally distributed with a mean of 76 (%) and standard deviation of 8 (%).
-In Professor Albert's course, students who earn less than a 60% in the class are assigned a failing grade (F). What proportion of the students earned F's? Report your answer with three decimal places.

Accepted Answer

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Question 11

Use the following to answer the questions below:
Final grades in Professor Albert's large calculus class are approximately normally distributed with a mean of 76 (%) and standard deviation of 8 (%).
-In Professor Albert's course, students who earn above a 94% are assigned an "A."What proportion of students earned A's? Report your answer with three decimal places.

Accepted Answer

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Question 12

Use the following to answer the questions below:
Final grades in Professor Albert's large calculus class are approximately normally distributed with a mean of 76 (%) and standard deviation of 8 (%).
-What proportion of students earn between an 82% and 88% in this class? Report your answer with three decimal places.

Accepted Answer

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Question 13

Use the following to answer the questions below:
Final grades in Professor Albert's large calculus class are approximately normally distributed with a mean of 76 (%) and standard deviation of 8 (%).
-What is the 25th percentile in this course? Report your answer with one decimal place.

Accepted Answer

The 25th percentile is the value below which 25% of the data falls. Using a standard normal distribution table, the z-score corresponding to the 25th percentile is -0.674. The corresponding value in the original distribution is 76 + (-0.674 * 8) = 70.6%.

Question 14

Use the following to answer the questions below:
Final grades in Professor Albert's large calculus class are approximately normally distributed with a mean of 76 (%) and standard deviation of 8 (%).
-The top 30% of students earned scores above what value? Report your answer with one decimal place.

Accepted Answer

The top 30% of students earned scores above the 70th percentile. Using a z-score table, the z-score corresponding to the 70th percentile is 0.52. The corresponding raw score is 76 + (0.52 * 8) = 79.8%.

Question 15

Use the following to answer the questions below:
Find the z* values based on a standard normal distribution for each of the following. Round to three decimal places.
-An 86% confidence interval for a proportion.

Accepted Answer

For an 86% confidence interval, the z* value corresponds to the middle 86% of the standard normal distribution. This leaves 7% in each tail (100% - 86% = 14%, divided by 2). The z* value for 0.07 in the lower tail is approximately 1.476.

Question 16

Use the following to answer the questions below:
Find the z* values based on a standard normal distribution for each of the following. Round to three decimal places.
-An 88% confidence interval for a correlation.

Accepted Answer

For an 88% confidence interval, the z* value corresponds to the middle 88% of the standard normal distribution, leaving 6% in each tail. The z* value for this is approximately 1.555.

Question 17

Use the following to answer the questions below:
Find the z* values based on a standard normal distribution for each of the following. Round to three decimal places.
-A 78% confidence interval for a mean.

Accepted Answer

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Question 18

Use the following to answer the questions below:
Find the z* values based on a standard normal distribution for each of the following. Round to three decimal places.
-A 66% confidence interval for a slope.

Accepted Answer

The z* value for a 66% confidence interval is 0.954.

Question 19

Use the following to answer the questions below:
A set of hypotheses, some information from one or more samples, and a standard error from a randomization distribution are provided. Find the value of the standardized z-test statistic.
-Test  : p = 0.75 versus  : p > 0.75 when the sample has   and

Accepted Answer

The answer of Use the following to answer the questions...

Question 20

Use the following to answer the questions below: A set of hypotheses, some information from one or more samples, and a standard error from a randomization distribution are provided. Find the value of the standardized z-test statistic. -Test :$\mu$ = 26 versus : $\mu$ $\neq$ 26 when the sample has n = 75, s = 5.4, and SE = 0.6.

Accepted Answer

The answer of Use the following to answer the questions...

Quiz 5: Approximating With a Distribution

Use the following to answer the questions below: Robins are common birds in North America. Suppose that the wingspan of robins is approximately normal with mean 14 inches and standard deviation 0.7 inches. -What is the 30th percentile of robin wingspans? Report your answer with two decimal places.

Use the following to answer the questions below: Final grades in Professor Albert's large calculus class are approximately normally distributed with a mean of 76 (%) and standard deviation of 8 (%). -Draw a sketch of this normal distribution and label at least three points on the horizontal axis.

Use the following to answer the questions below: Final grades in Professor Albert's large calculus class are approximately normally distributed with a mean of 76 (%) and standard deviation of 8 (%) . -What is the 25th percentile in this course? Report your answer with one decimal place.

Use the following to answer the questions below: Final grades in Professor Albert's large calculus class are approximately normally distributed with a mean of 76 (%) and standard deviation of 8 (%) . -The top 30% of students earned scores above what value? Report your answer with one decimal place.

Use the following to answer the questions below: Find the z* values based on a standard normal distribution for each of the following. Round to three decimal places. -An 86% confidence interval for a proportion.

Use the following to answer the questions below: Find the z* values based on a standard normal distribution for each of the following. Round to three decimal places. -An 88% confidence interval for a correlation.

Use the following to answer the questions below: Find the z* values based on a standard normal distribution for each of the following. Round to three decimal places. -A 78% confidence interval for a mean.

Use the following to answer the questions below: Find the z* values based on a standard normal distribution for each of the following. Round to three decimal places. -A 66% confidence interval for a slope.

Use the following to answer the questions below: A set of hypotheses, some information from one or more samples, and a standard error from a randomization distribution are provided. Find the value of the standardized z-test statistic. -Test : p = 0.75 versus : p > 0.75 when the sample has and