he number of chocolate chips in an 18-ounce bag of Chips Ahoy! chocolate chip cookies is approximately normally distributed, with a mean of 1262 chips and a standard deviation of 118 chips, according to a study by cadets of the U.S. Air Force Academy. (a) Determine the 28th percentile for the number of chocolate chips in an 18-ounce bag of Chips Ahoy! cookies. (b) Determine the number of chocolate chips in a bag of Chips Ahoy! that make up the middle 98% of bags. (c) What is the interquartile range of the number of chips in Chips Ahoy! cookies?
he number of chocolate chips in an 18-ounce bag of Chips Ahoy! chocolate chip cookies is approximately normally distributed, with a mean of 1262 chips and a standard deviation of 118 chips, according to a study by cadets of the U.S. Air Force Academy. (a) Determine the 28th percentile for the number of chocolate chips in an 18-ounce bag of Chips Ahoy! cookies. (b) Determine the number of chocolate chips in a bag of Chips Ahoy! that make up the middle 98% of bags. (c) What is the interquartile range of the number of chips in Chips Ahoy! cookies?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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The number of chocolate chips in an 18-ounce bag of Chips Ahoy! chocolate chip cookies is approximately
(a) Determine the 28th percentile for the number of chocolate chips in an 18-ounce bag of Chips Ahoy! cookies.
(b) Determine the number of chocolate chips in a bag of Chips Ahoy! that make up the middle 98% of bags.
(c) What is the interquartile range of the number of chips in Chips Ahoy! cookies?
Transcribed Image Text:### Standard Normal Distribution Table
This table presents values of the cumulative distribution function (CDF) for the standard normal distribution. Each cell value represents the probability that a standard normal random variable \( Z \) is less than or equal to the corresponding z-score.
The table is organized as follows:
- **Rows and Columns**: The rows represent the first digit and the first decimal place of the z-score (ranging from 0.0 to 2.4), and the columns represent the second decimal place of the z-score. For example, the z-score 0.56 consists of the row value 0.5 and the column value 0.06.
- **Cell Values**: Each cell shows the probability \( P(Z \leq z) \).
#### Using the Table
To find the probability for a specific z-score:
1. **Identify the z-score**: Break it into the first digit and first decimal (row) and the second decimal (column).
2. **Locate the Probability**: Find the intersection of the corresponding row and column.
#### Example
For \( z = 0.67 \):
- Find the row for 0.6.
- Find the column for 0.07.
- The cell at the intersection provides the probability: 0.7486.
The table allows easy look-up of probabilities associated with z-scores, essential for statistical analyses involving the standard normal distribution.
Transcribed Image Text:The image contains a Z-table, which is used in statistics to find the probability of a standard normal distribution curve to the left of a given Z-score. This is often used in hypothesis testing and confidence interval estimation.
### Table Structure:
- **Rows:** Indicate the integer and first decimal place of the Z-score (e.g., -2.4, -2.3, etc.).
- **Columns:** Represent the second decimal place of the Z-score (e.g., 0.00, 0.01, etc.), although the table only shows from 0.00 to 0.09.
### Entries:
Each cell within the table provides the cumulative probability for a specific Z-score. The probability is the area under the normal curve to the left of the specified Z-score. For example:
- A Z-score of -2.4 and a second decimal of 0.00 results in a cumulative probability of 0.0082.
- A Z-score of -1.0 and a second decimal of 0.03 yields a cumulative probability of 0.1446.
These values can quickly show how likely an observation is in a normal distribution with respect to its mean.
### Usage:
The Z-table is essential for statistical analysis, allowing us to understand the probability distribution of a dataset and make informed decisions based on the data.
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