Given that z is a standard normal random variable, find z for each situation (to 2 decimals). a. The area to the right of z is 0.02. -2.05 0 b. The area to the right of z is 0.045. -0.13 0 c. The area to the right of z is 0.05. -1.65 0 d. The area to the right of z is 0.40. -0.25 0 Suppose that the mean daily viewing time of television is 8.35 hours per household. Use a normal probability distribution with a standard deviation of 2.5 hours to answer the following questions about daily television viewing per household. 3. What is the probability that a household views television between 3 and 9 hours a day (to 4 decimals)? b. How many hours of television viewing must a household have in order to be in the top 4% of all television viewing households (to 2 decimals)? ' hours c. What is the probability that a household views television more than 4 hours a day (to 4 decimals)? Alexa is the popular virtual assistant developed by Amazon. Alexa interacts with users using articial 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)? 0 b. What is the probability there are between 1,500 and 2,500 downloads of Amazon Alexa in a day (to 4 decimals)? -0 c. What is the probability there are more than 3,000 downloads of Amazon Alexa in a day (to 4 decimals)? -0 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 nearest whole number)? -9