The number of orders received daily by an online vendor of used CDs is normally distributed with mean 300 and standard deviation 20. The company has to hire extra help or pay overtime on those days when the number of orders received is 344 or higher. What percentage of days will the company have to hire extra help or pay overtime? Click the icon to view the standard normal distribution table. - X Areas for a Standard Normal Distribution The company will have to hire extra help or pay overtime on % of days. Entries in the table represent area under the curve between z=0 and a positive value of z. Because of the symmetry of the curve, area under the curve between z = 0 and a negative value of z would be found in a similar manner. z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.0000 0.0040 0.0080 0.0120 0.0160 0.0199 0.0239 0.0279 0.0319 0.0359 0.1 0.0398 0.0438 0.0478 0.0517 0.0557 0.0596 0.0636 0.0675 0.0714 0.0753 0.2 0.0793 0.0832 0.0871 0.0910 0.0948 0.0987 0.1026 0.1064 0.1103 0.1141 0.3 0.1179 0.1217 0.1255 0.1293 0.1331 0.1368 0.1406 0.1443 0.1480 0.1517 0.4 0.1554 0.1591 0.1628 0.1664 0.1700 0.1736 0.1772 0.1808 0.1844 0.1879 0.5 0.1915 0.1950 0.1985 0.2019 0.2054 0.2088 0.2123 0.2157 0.2190 0.2224 0.6 0.2257 0.2291 0.2324 0.2357 0.2389 0.2422 0.2454 0.2486 0.2517 0.2549 0.7 0.2580 0.2611 0.2642 0.2673 0.2704 0.2734 0.2764 0.2794 0.2823 0.2852 0.8 0.2881 0.2910 0.2939 0.2967 0.2995 0.3023 0.3051 0.3078 0.3106 0.3133 0.9 0.3159 0.3186 0.3212 0.3238 0.3264 0.3289 0.3315 0.3340 0.3365 0.3389 1.0 0.3413 0.3438 0.3461 0.3485 0.3508 0.3531 0.3554 0.3577 0.3599 0.3621 1.1 0.3643 0.3665 0.3686 0.3708 0.3729 0.3749 0.3770 0.3790 0.3810 0.3830 1.2 0.3849 0.3869 0.3888 0.3907 0.3925 0.3944 0.3962 0.3980 0.3997 0.4015 1.3 0.4032 0.4049 0.4066 0.4082 0.4099 0.4115 0.4131 0.4147 0.4162 0.4177 1.4 0.4192 0.4207 0.4222 0.4236 0.4251 0.4265 0.4279 0.4292 0.4306 0.4319 1.5 0.4332 0.4345 0.4357 0.4370 0.4382 0.4394 0.4406 0.4418 0.4429 0.4441 1.6 0.4452 0.4463 0.4474 0.4484 0.4495 0.4505 0.4515 0.4525 0.4535 0.4545 1.7 0.4554 0.4564 0.4573 0.4582 0.4591 0.4599 0.4608 0.4616 0.4625 0.4633 1.8 0.4641 0.4649 0.4656 0.4664 0.4671 0.4678 0.4686 0.4693 0.4699 0.4706 1.9 0.4713 0.4719 0.4726 0.4732 0.4738 0.4744 0.4750 0.4756 0.4761 0.4767 2.0 0.4772 0.4778 0.4783 0.4788 0.4793 0.4798 0.4803 0.4808 0.4812 0.4817 2.1 0.4821 0.4826 0.4830 0.4834 0.4838 0.4842 0.4846 0.4850 0.4854 0.4857 2.2 0.4861 0.4864 0.4868 0.4871 0.4875 0.4878 0.4881 0.4884 0.4887 0.4890 2.3 0.4893 0.4896 0.4898 0.4901 0.4904 0.4906 0.4909 0.4911 0.4913 0.4916 2.4 0.4918 0.4920 0.4922 0.4925 0.4927 0.4929 0.4931 0.4932 0.4934 0.4936 2.5 0.4938 0.4940 0.4941 0.4943 0.4945 0.4946 0.4948 0.4949 0.4951 0.4952 2.6 0.4953 0.4955 0.4956 0.4957 0.4959 0.4960 0.4961 0.4962 0.4963 0.4964 2.7 0.4965 0.4966 0.4967 0.4968 0.4969 0.4970 0.4971 0.4972 0.4973 0.4974 2.8 0.4974 0.4975 0.4976 0.4977 0.4977 0.4978 0.4979 0.4979 0.4980 0.4981 2.9 0.4981 0.4982 0.4982 0.4983 0.4984 0.4984 0.4985 0.4985 0.4986 0.4986 30h 1987 04987 04987 4988 1988 0.4989 04989 04989 0499004990

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**Understanding Standard Normal Distribution and its Applications**

**Problem Statement:**
The number of orders received daily by an online vendor of used CDs is normally distributed with a mean of 300 and a standard deviation of 20. The company has to hire extra help or pay overtime on those days when the number of orders received is 344 or higher. What percentage of days will the company have to hire extra help or pay overtime?

**Solution Steps:**

1. Calculate the z-score:
   The z-score is given by the formula:
   \[ z = \frac{X - \mu}{\sigma} \]
   where \( X \) is the value (344), \( \mu \) is the mean (300), and \( \sigma \) is the standard deviation (20).

2. Applying the values:
   \[ z = \frac{344 - 300}{20} = \frac{44}{20} = 2.2 \]

3. Using the Standard Normal Distribution Table:
   Click the icon to view the standard normal distribution table and find the area under the curve corresponding to \( z = 2.2 \).

**Areas for a Standard Normal Distribution Table Explanation:**

An accompanying table helps to find the probability values for different z-scores. The table used here lists z-scores in increments (0.00, 0.01, … up to 3.0), denoting areas under the standard normal curve. Each entry provides the probability for z-scores ranging from 0 up to the positive z-value given.

**Table Excerpt:**
|   z   | 0.00  | 0.01  | 0.02  | 0.03  | 0.04  | 0.05  | 0.06  | 0.07  | 0.08  | 0.09  |
|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|
| 2.0   | 0.4772| 0.4783| 0.4793| 0.4803| 0.4812| 0.4821| 0.4830| 0.4838| 0.4846| 0.4854|
| 2.1   | 0.4880| 0.4888|
Transcribed Image Text:**Understanding Standard Normal Distribution and its Applications** **Problem Statement:** The number of orders received daily by an online vendor of used CDs is normally distributed with a mean of 300 and a standard deviation of 20. The company has to hire extra help or pay overtime on those days when the number of orders received is 344 or higher. What percentage of days will the company have to hire extra help or pay overtime? **Solution Steps:** 1. Calculate the z-score: The z-score is given by the formula: \[ z = \frac{X - \mu}{\sigma} \] where \( X \) is the value (344), \( \mu \) is the mean (300), and \( \sigma \) is the standard deviation (20). 2. Applying the values: \[ z = \frac{344 - 300}{20} = \frac{44}{20} = 2.2 \] 3. Using the Standard Normal Distribution Table: Click the icon to view the standard normal distribution table and find the area under the curve corresponding to \( z = 2.2 \). **Areas for a Standard Normal Distribution Table Explanation:** An accompanying table helps to find the probability values for different z-scores. The table used here lists z-scores in increments (0.00, 0.01, … up to 3.0), denoting areas under the standard normal curve. Each entry provides the probability for z-scores ranging from 0 up to the positive z-value given. **Table Excerpt:** | z | 0.00 | 0.01 | 0.02 | 0.03 | 0.04 | 0.05 | 0.06 | 0.07 | 0.08 | 0.09 | |-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------| | 2.0 | 0.4772| 0.4783| 0.4793| 0.4803| 0.4812| 0.4821| 0.4830| 0.4838| 0.4846| 0.4854| | 2.1 | 0.4880| 0.4888|
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