Assume that the traffic to the web site of Smiley's People, Inc., which sells customized T-shirts, follows a normal distribution, with a mean of 4.6 million visitors per day and a standard deviation of 880,000 visitors per day. (a) What is the probability that the web site has fewer than 5 million visitors in a single day? If needed, round your answer to four decimal digits. (b) What is the probability that the web site has 3 million or more visitors in a single day? If needed, round your answer to four decimal digits. (c) What is the probability that the web site has between 3 million and 4 million visitors in a single day? If needed, round your answer to four decimal digits. (d) Assume that 85% of the time, the Smiley's People web servers fan handle the daily web traffic volume without purchasing additional server capacity. What is the amount of web traffic that will require Smiley's People to purchase additional server capacity? If needed, round your answer to two decimal digits. million visitors per day

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
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Need help on parts A, B, C, & D (I.E. all blank text-boxes)
**Normal Distribution Traffic Analysis for Smiley's People, Inc. Website**

Smiley's People, Inc., which sells customized T-shirts online, experiences web traffic that follows a normal distribution. The daily mean visitor count is 4.6 million, with a standard deviation of 880,000 visitors.

**Tasks:**

(a) **Probability of Fewer than 5 Million Visitors:**
Calculate the probability that the website has fewer than 5 million visitors in a single day. Round your answer to four decimal digits if necessary.

(b) **Probability of 3 Million or More Visitors:**
Determine the probability that the website has 3 million or more visitors in a single day. Round your answer to four decimal digits if needed.

(c) **Probability Between 3 Million and 4 Million Visitors:**
Find the probability that the website has between 3 million and 4 million visitors in a single day. Round your answer to four decimal digits if required.

(d) **Server Capacity Threshold:**
Assuming Smiley’s People web servers can handle the daily web traffic volume 85% of the time without purchasing additional server capacity, calculate the visitor count threshold that would necessitate additional capacity. Round your answer to two decimal digits if needed.

**Note:** Use statistical tools to calculate probabilities and thresholds based on the normal distribution parameters given (mean = 4.6 million, standard deviation = 880,000).
Transcribed Image Text:**Normal Distribution Traffic Analysis for Smiley's People, Inc. Website** Smiley's People, Inc., which sells customized T-shirts online, experiences web traffic that follows a normal distribution. The daily mean visitor count is 4.6 million, with a standard deviation of 880,000 visitors. **Tasks:** (a) **Probability of Fewer than 5 Million Visitors:** Calculate the probability that the website has fewer than 5 million visitors in a single day. Round your answer to four decimal digits if necessary. (b) **Probability of 3 Million or More Visitors:** Determine the probability that the website has 3 million or more visitors in a single day. Round your answer to four decimal digits if needed. (c) **Probability Between 3 Million and 4 Million Visitors:** Find the probability that the website has between 3 million and 4 million visitors in a single day. Round your answer to four decimal digits if required. (d) **Server Capacity Threshold:** Assuming Smiley’s People web servers can handle the daily web traffic volume 85% of the time without purchasing additional server capacity, calculate the visitor count threshold that would necessitate additional capacity. Round your answer to two decimal digits if needed. **Note:** Use statistical tools to calculate probabilities and thresholds based on the normal distribution parameters given (mean = 4.6 million, standard deviation = 880,000).
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