Data Management (MDM4U) · Statistical Analysis

Normal distribution: the 68-95-99.7 rule

Apply the 68-95-99.7 rule to estimate percentages and counts for a normally distributed variable. Unlimited questions, five difficulty levels, and a full worked solution every time, included free with weekly lessons.

Practice this skill Curriculum: MDM4U-SA1.3

Try one

The battery life of a popular phone model is approximately normally distributed with mean 11 hours and standard deviation 1 hours. Using the 68-95-99.7 rule, about what percent of values fall between 9 and 13 hours?

Answer: 95

See one solved, step by step

The time it takes students to finish a standardized test is approximately normally distributed with mean 60 minutes and standard deviation 10 minutes. Using the 68-95-99.7 rule, about what percent of values fall between 30 and 90 minutes?

📘 Worked solution

160 - 3(10) = 30, 60 + 3(10) = 90Find the boundary values, which are 3 standard deviations away from the mean on each side.

2About 99.7% of a normal distribution lies within 3 standard deviations of the mean.That's the 68-95-99.7 rule: 68% within 1 SD, 95% within 2 SD, 99.7% within 3 SD.

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