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Home » Distance from $(1,1,0)$: - DevRocket

Distance from $(1,1,0)$: - DevRocket

📅 May 2, 2026 👤 scraface

May 02, 2026

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📌 Standard deviation: \( \sqrt{30} \approx 5.477 \) → rounds to 5.5

📌 A UX designer is optimizing a form that has 6 input fields. The average time users take to complete the form is 90 seconds, based on a sample of 200 users. If a new prototype reduces the time per field by 15%, and each field contributes equally, what is the new average completion time?

📌 Original average time per field: \( \frac{90}{6} = 15 \) seconds

📌 15% reduction: \( 15 \times 0.85 = 12.75 \) seconds per field

📌 New total time: \( 6 \times 12.75 = 76.5 \) seconds

📌 An epidemiologist models recovery time from an illness using a normal distribution with mean 14 days and standard deviation 3 days. What percentage of patients recover in more than 20 days? (Use the 68-95-99.7 rule and appropriate z-score calculation.)

📌 \( z = \frac{20 - 14}{3} = 2 \)

📌 95% of data within \( \pm 2\sigma \), so 5% outside

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