The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with mean 1252 and standard deviation 129 chips. (a) What is the probability that a randomly selected bag contains between 1100 and 1500 chocolate chips? (b) What is the probability that a randomly selected bag contains fewer than 1100 chocolate chips? (c) What proportion of bags contains more than 1225 chocolate chips? (d) What is the percentile rank of a bag that contains 1450 chocolate chips? Click the icon to view a table of areas under the normal curve. (a) The probability that a randomly selected bag contains between 1100 and 1500 chocolate chips is (Round to four decimal places as needed.)
The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with mean 1252 and standard deviation 129 chips. (a) What is the probability that a randomly selected bag contains between 1100 and 1500 chocolate chips? (b) What is the probability that a randomly selected bag contains fewer than 1100 chocolate chips? (c) What proportion of bags contains more than 1225 chocolate chips? (d) What is the percentile rank of a bag that contains 1450 chocolate chips? Click the icon to view a table of areas under the normal curve. (a) The probability that a randomly selected bag contains between 1100 and 1500 chocolate chips is (Round to four decimal places as needed.)
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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Transcribed Image Text:The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with a mean of 1252 and a standard deviation of 129 chips.
(a) What is the probability that a randomly selected bag contains between 1100 and 1500 chocolate chips?
(b) What is the probability that a randomly selected bag contains fewer than 1100 chocolate chips?
(c) What proportion of bags contains more than 1225 chocolate chips?
(d) What is the percentile rank of a bag that contains 1450 chocolate chips?
To solve these questions, click the icon to view a table of areas under the normal curve.
Question (a) specifically asks for the probability that a randomly selected bag contains between 1100 and 1500 chocolate chips. The space provided indicates that the answer should be rounded to four decimal places as needed.
Transcribed Image Text:**Standard Normal Distribution Table (Z-Table)**
This table displays the cumulative probability of the standard normal distribution. The standard normal distribution, often represented by a symmetrical bell curve, is a continuous probability distribution that is symmetric around its mean.
### Table V: Standard Normal Distribution
The table provides the area under the standard normal curve to the left of a given Z-value. The Z-values are typically found on the leftmost column and the top row of the table. Each cell shows the cumulative probability associated with that Z-value.
#### Reading the Table:
- **Z-value:** Find the Z-value to two decimal places using the left column for the first decimal and the top row for the second decimal.
- **Probability:** The corresponding cell value is the probability that a standard normal random variable is less than or equal to the given Z-value.
For example, a Z-value of -0.5 corresponds to a cumulative probability of 0.3085.
### Diagram:
The top left part of the image contains a diagram illustrating a normal distribution curve.
- **X-axis:** Represents the Z-values.
- **Area:** The shaded portion under the curve corresponds to the probability of the random variable falling within that range.
- This diagram helps conceptualize how areas under the curve relate to cumulative probabilities.
The standard normal distribution is fundamental in statistics, enabling calculations related to areas under the curve, z-scores, and probabilities for a normally distributed dataset.
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