Alexa is the popular virtual assistant developed by Amazon. Alexa interacts with users using artificial intelligence and voice recognition. It can be used to perform daily tasks such as making to-do lists, reporting the news and weather, and interacting with other smart devices in the home. In 2018, the Amazon Alexa app was downloaded some 2,800 times per day from the Google Play store (AppBrain website). Assume that the number of downloads per day of the Amazon Alexa app is normally distributed with a mean of 2,800 and standard deviation of 860. a. What is the probability there are 2,000 or fewer downloads of Amazon Alexa in a day (to 4 decimals)? b. What is the probability there are between 1,500 and 2,500 downloads of Amazon Alexa in a day (to 4 decimals)? c. What is the probability there are more than 3,000 downloads of Amazon Alexa in a day (to 4 decimals)? d. Assume that Google has designed its servers so there is probability 0.01 that the number of Amazon Alexa app downloads in a day exceeds the servers' capacity and more servers have to be brought online. How many Amazon Alexa app downloads per day are Google's servers designed to handle (to the neares whole number)?
Alexa is the popular virtual assistant developed by Amazon. Alexa interacts with users using artificial intelligence and voice recognition. It can be used to perform daily tasks such as making to-do lists, reporting the news and weather, and interacting with other smart devices in the home. In 2018, the Amazon Alexa app was downloaded some 2,800 times per day from the Google Play store (AppBrain website). Assume that the number of downloads per day of the Amazon Alexa app is normally distributed with a mean of 2,800 and standard deviation of 860. a. What is the probability there are 2,000 or fewer downloads of Amazon Alexa in a day (to 4 decimals)? b. What is the probability there are between 1,500 and 2,500 downloads of Amazon Alexa in a day (to 4 decimals)? c. What is the probability there are more than 3,000 downloads of Amazon Alexa in a day (to 4 decimals)? d. Assume that Google has designed its servers so there is probability 0.01 that the number of Amazon Alexa app downloads in a day exceeds the servers' capacity and more servers have to be brought online. How many Amazon Alexa app downloads per day are Google's servers designed to handle (to the neares whole number)?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![**Title: Understanding Probability Distributions: A Case Study with Amazon Alexa Downloads**
**Introduction:**
Amazon Alexa is a popular virtual assistant that integrates artificial intelligence and voice recognition. It helps users with tasks such as creating to-do lists, providing news and weather updates, and controlling smart home devices. In 2018, the Amazon Alexa app was downloaded approximately 2,800 times daily from the Google Play store according to AppBrain data. This case study explores the probability distribution of Alexa app downloads, assuming a normal distribution with a mean of 2,800 and a standard deviation of 860.
---
**Questions:**
1. **Probability of 2,000 or Fewer Downloads:**
Calculate the probability that there are 2,000 or fewer downloads of the Amazon Alexa app in a day. Provide your answer to four decimal places.
\[ \text{Probability:} \, \_\_\_\_\_ \]
2. **Probability Between 1,500 and 2,500 Downloads:**
Determine the probability that daily downloads are between 1,500 and 2,500. Provide your answer to four decimal places.
\[ \text{Probability:} \, \_\_\_\_\_ \]
3. **Probability of More Than 3,000 Downloads:**
What is the probability that there are more than 3,000 downloads in a day? Provide your answer to four decimal places.
\[ \text{Probability:} \, \_\_\_\_\_ \]
4. **Server Capacity Planning:**
Assume Google designed its servers to ensure the probability is 0.01 that the number of daily downloads exceeds server capacity, necessitating additional resources. How many downloads are Google’s servers prepared to handle? Round your answer to the nearest whole number.
\[ \text{Download Capacity:} \, \_\_\_\_\_ \]
---
**Conclusion:**
This exercise demonstrates the application of normal distribution in forecasting and capacity planning, using the example of Amazon Alexa app downloads. Understanding these probabilities helps in efficient resource management and service optimization.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffa11c8a8-eb56-4157-9233-facd50115ae0%2F529e8f84-9943-47f3-8be3-f9d35163be66%2Fhohempg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Understanding Probability Distributions: A Case Study with Amazon Alexa Downloads**
**Introduction:**
Amazon Alexa is a popular virtual assistant that integrates artificial intelligence and voice recognition. It helps users with tasks such as creating to-do lists, providing news and weather updates, and controlling smart home devices. In 2018, the Amazon Alexa app was downloaded approximately 2,800 times daily from the Google Play store according to AppBrain data. This case study explores the probability distribution of Alexa app downloads, assuming a normal distribution with a mean of 2,800 and a standard deviation of 860.
---
**Questions:**
1. **Probability of 2,000 or Fewer Downloads:**
Calculate the probability that there are 2,000 or fewer downloads of the Amazon Alexa app in a day. Provide your answer to four decimal places.
\[ \text{Probability:} \, \_\_\_\_\_ \]
2. **Probability Between 1,500 and 2,500 Downloads:**
Determine the probability that daily downloads are between 1,500 and 2,500. Provide your answer to four decimal places.
\[ \text{Probability:} \, \_\_\_\_\_ \]
3. **Probability of More Than 3,000 Downloads:**
What is the probability that there are more than 3,000 downloads in a day? Provide your answer to four decimal places.
\[ \text{Probability:} \, \_\_\_\_\_ \]
4. **Server Capacity Planning:**
Assume Google designed its servers to ensure the probability is 0.01 that the number of daily downloads exceeds server capacity, necessitating additional resources. How many downloads are Google’s servers prepared to handle? Round your answer to the nearest whole number.
\[ \text{Download Capacity:} \, \_\_\_\_\_ \]
---
**Conclusion:**
This exercise demonstrates the application of normal distribution in forecasting and capacity planning, using the example of Amazon Alexa app downloads. Understanding these probabilities helps in efficient resource management and service optimization.
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