Part D only please and solve without using excel only the Normal Curve table

MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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Part D only please and solve without using excel only the Normal Curve table
The image depicts a standard normal distribution table, often used in statistics to determine the probability of a value occurring within a normal distribution. Each entry in the table corresponds to the cumulative probability of a standard normal variable z.

### Explanation of the Table:

#### Structure:
- The table is organized with z-scores displayed in the first column and the top row. 
- The first column contains the integer and first decimal place of the z-score, ranging from 0.0 to at least 3.6.
- The top row includes the second decimal place of the z-score, ranging from .00 to .09.

#### Content:
- The cell at the intersection of a row and a column gives the cumulative probability for the corresponding z-score.
- For example, the intersection at z = 0.0 and .01 (0.01) gives a probability of 0.0038, indicating that 0.38% of the data lies below this z-score.
- The values increase as you move rightward across a row or downward down a column, representing higher cumulative probabilities.

#### Usage:
- This table is vital for determining z-scores in various statistical analyses, allowing one to ascertain probabilities related to specific data points within a standard normal distribution.
- It is particularly useful in hypothesis testing and confidence interval estimation.

### No Graphs or Diagrams:
- The table includes no graphs or additional diagrams. It purely lists numerical values related to the standard normal distribution.
Transcribed Image Text:The image depicts a standard normal distribution table, often used in statistics to determine the probability of a value occurring within a normal distribution. Each entry in the table corresponds to the cumulative probability of a standard normal variable z. ### Explanation of the Table: #### Structure: - The table is organized with z-scores displayed in the first column and the top row. - The first column contains the integer and first decimal place of the z-score, ranging from 0.0 to at least 3.6. - The top row includes the second decimal place of the z-score, ranging from .00 to .09. #### Content: - The cell at the intersection of a row and a column gives the cumulative probability for the corresponding z-score. - For example, the intersection at z = 0.0 and .01 (0.01) gives a probability of 0.0038, indicating that 0.38% of the data lies below this z-score. - The values increase as you move rightward across a row or downward down a column, representing higher cumulative probabilities. #### Usage: - This table is vital for determining z-scores in various statistical analyses, allowing one to ascertain probabilities related to specific data points within a standard normal distribution. - It is particularly useful in hypothesis testing and confidence interval estimation. ### No Graphs or Diagrams: - The table includes no graphs or additional diagrams. It purely lists numerical values related to the standard normal distribution.
**4.99 DELIVERY TIMES FOR ONLINE ORDERS**

Refer to the *Journal of Marketing Research* (October 2019) study of delivery times for online orders, Exercise 2.88 (p. 88). Recall that a major apparel retailer has two distribution centers (DCs) to fulfill all its online orders—one located in the eastern United States and one in the western United States. Based on the study, we can assume that the delivery time \(x\) (in business days) for online orders fulfilled by the eastern DC is normally distributed with mean \(\mu = 5.22\) and standard deviation \(\sigma = 0.77\). Similarly, assume that the delivery time \(x\) for online orders fulfilled by the western DC is normally distributed with mean \(\mu = 6.95\) and standard deviation \(\sigma = 0.55\).

- **a.** For online orders filled by the eastern DC, find \(P(x \leq 5)\).
- **b.** For online orders filled by the eastern DC, find \(P(4 \leq x \leq 7)\).

- **c.** For online orders filled by the eastern DC, find the value \(a\), so that \(P(x > a) = 0.30\).

- **d.** Repeat parts a-c for online orders filled by the western DC.
Transcribed Image Text:**4.99 DELIVERY TIMES FOR ONLINE ORDERS** Refer to the *Journal of Marketing Research* (October 2019) study of delivery times for online orders, Exercise 2.88 (p. 88). Recall that a major apparel retailer has two distribution centers (DCs) to fulfill all its online orders—one located in the eastern United States and one in the western United States. Based on the study, we can assume that the delivery time \(x\) (in business days) for online orders fulfilled by the eastern DC is normally distributed with mean \(\mu = 5.22\) and standard deviation \(\sigma = 0.77\). Similarly, assume that the delivery time \(x\) for online orders fulfilled by the western DC is normally distributed with mean \(\mu = 6.95\) and standard deviation \(\sigma = 0.55\). - **a.** For online orders filled by the eastern DC, find \(P(x \leq 5)\). - **b.** For online orders filled by the eastern DC, find \(P(4 \leq x \leq 7)\). - **c.** For online orders filled by the eastern DC, find the value \(a\), so that \(P(x > a) = 0.30\). - **d.** Repeat parts a-c for online orders filled by the western DC.
Expert Solution
Step 1

Given that:

For eastern DC, the mean and standard deviation are:

μ=5.22σ=0.77

For western DC, the mean and standard deviation are:

μ=6.95σ=0.55

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