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 2800 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 2800 and standard deviation of 860. 

a. What is the probability there are 2000 or fewer downloads of Amazon Alexa in a day? 

b. What is the probability there are between 1500 and 2500 downloads of Amazon Alexa in a day? 

c. What is the probability there are more than 3000 downloads of Amazon Alexa in a day? 

d. Assume that Google has designed its servers so there is probability .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?