Standard normal table for proportion between values | AP Statistics | Khan Academy

TL;DR

The video explains how to calculate the proportion of laptop prices that fall between $624 and $768 in a normally distributed dataset.

Transcript

• [Instructor] A set of laptop prices are normally distributed with a mean of $750 and a standard deviation of $60. What proportion of laptop prices are between $624 and $768? So let's think about what they are asking. So we have a normal distribution for the prices. So it would look something like this. This is just my hand-drawn sketch of a norma... Read More

Key Insights

• 🤪 The video teaches how to calculate proportions in a normal distribution using z-scores and a z-table.
• ❓ The spread of data above and below the mean can be represented by standard deviations.
• 🤪 Z-scores provide a standardized way to compare values in a normal distribution.

Questions & Answers

Q: How is the normal distribution of laptop prices represented in the video?

The video presents a hand-drawn sketch of a normal distribution, with the mean represented by the center and the standard deviation showing the spread of prices above and below the mean.

Q: How is the z-score calculated for the upper bound of $768?

The z-score is calculated by subtracting the mean of $750 from $768 and dividing the result by the standard deviation of $60, resulting in a z-score of 0.30.

Q: How is the proportion of laptop prices less than $768 determined using the z-table?

The z-score of 0.30 is located in the z-table, which corresponds to a proportion of 0.6179. This represents the area under the normal distribution curve up to $768.

Q: How is the z-score calculated for the lower bound of $624?

The z-score is calculated by subtracting the mean of $750 from $624 and dividing the result by the standard deviation of $60, resulting in a z-score of -2.10.

Q: What proportion of laptop prices is below $624?

The z-score of -2.10 is located in the z-table, which corresponds to a proportion of 0.0179. This represents the area under the normal distribution curve up to $624.

Q: How is the proportion of laptop prices between $624 and $768 calculated?

To calculate the proportion between the two values, the proportion below $768 (0.6179) is subtracted from the proportion below $624 (0.0179), resulting in a proportion of 0.6000 or 60%.

Summary & Key Takeaways

• The video discusses a normal distribution of laptop prices with a mean of $750 and a standard deviation of $60.

• To find the proportion of laptop prices between $624 and $768, z-scores are calculated for both values and then referenced in a z-table.

• The proportion of laptop prices between $624 and $768 is found to be 0.6000 or 60%.