Question

The test scores for a class have a normal distribution, a mean of $50,$ and a standard deviation of 4. Quantity $\mathbf{A}$ Percentage of scores at or above 58 Quantity $\mathbf{B}$ Percentage of scores at or below 42 a. Quantity A is greater b. Quantity B is greater. c. The two quantities are equal. d. The relationship cannot be determined from the information given.

Name: Problem 3, Chapter :
Uploaded: 2020-07-23T20:23:08-08:00
Duration: 1 min 2 s
Channel: Heather Zimmers
Description: The test scores for a class have a normal distribution, a mean of 50, and a standard deviation of 4. Quantity 𝐀 Percentage of scores at or above 58 Quantity 𝐁 Percentage of scores at or below 42 a. Quantity A is greater b. Quantity B is greater. c. The two quantities are equal. d. The relationship cannot be determined from the information given.

   The test scores for a class have a normal distribution, a mean of $50,$ and a standard deviation of 4.
Quantity $\mathbf{A}$
Percentage of scores at or above 58
Quantity $\mathbf{B}$
Percentage of scores at or below 42
a. Quantity A is greater
b. Quantity B is greater.
c. The two quantities are equal.
d. The relationship cannot be determined from the information given.

Instant Answer

Solved by Expert Heather Zimmers

07/23/2020

Step 1

In a normal distribution, the mean, median, and mode are all equal and located at the center of the distribution. The distribution is symmetric about the mean. Show more…

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The test scores for a class have a normal distribution, a mean of $50,$ and a standard deviation of 4. Quantity $\mathbf{A}$ Percentage of scores at or above 58 Quantity $\mathbf{B}$ Percentage of scores at or below 42 a. Quantity A is greater b. Quantity B is greater. c. The two quantities are equal. d. The relationship cannot be determined from the information given.

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Key Concepts

Normal Distribution

A normal distribution is a bell-shaped probability distribution that is symmetrical about its mean. It is characterized by its mean and standard deviation, which dictate the center and spread of the data, respectively.

Z-Score

A z-score measures how many standard deviations a data point is from the mean. Converting data points to z-scores allows for comparison across different normal distributions by placing them on a standardized scale.

Symmetry of the Normal Distribution

The symmetry of the normal distribution means that data points equidistant from the mean have equal probabilities. This property implies that the percentage of data above a certain value above the mean is equal to the percentage below a corresponding value below the mean.

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