Normal Distribution Worksheets Grade 11

1. Normal: μ=68, σ=4. What % between 60 and 76?
2. Charlotte is analyzing the lifespans of a particular model of LED light bulb produced by her company. The lifespans (in hours) are normally distributed with a mean of 12,000 hours and a standard deviation of 2,000 hours. The company's marketing department wants to advertise a 'long-life' warranty that covers the top 2.5% of bulbs. What is the minimum number of hours a bulb must last to qualify for this 'long-life' warranty?
3. A right triangle is drawn on a coordinate plane with vertices at (0,0), (6,0), and (6,8). A circle is circumscribed around this triangle such that all three vertices lie on the circle's circumference. What is the area of this circumscribed circle?

…and 4 more problems

1. Sophia is analyzing the scores from a national mathematics competition. The scores are normally distributed with a mean of 61 points and a standard deviation of 6 points. The top 16% of students receive a certificate of excellence. Using the 68-95-99.7 rule, determine the minimum score a student must achieve to earn the certificate.
2. A pharmaceutical company tests a new medication and finds the recovery times for patients follow a normal distribution with a mean of 14 days and a standard deviation of 2.5 days. Dr. Chen is treating a patient who recovered in 19 days. What percentage of patients would be expected to recover in more time than Dr. Chen's patient?
3. A triangular prism has a right triangle base with legs measuring 6 cm and 8 cm, and a height of 15 cm. The prism is positioned so that the triangular bases are vertical. What is the total surface area of this prism?

…and 4 more problems

1. Olivia is a quality control analyst at a battery manufacturing plant. The lifespan of the batteries produced follows a normal distribution with a mean of 450 hours and a standard deviation of 15 hours. The company guarantees that batteries will last at least 420 hours. Using the 68-95-99.7 rule, what percentage of batteries will fail to meet this guarantee (i.e., have a lifespan less than 420 hours)?
2. Charlotte is analyzing the annual snowfall amounts in a mountain town. The snowfall amounts follow a normal distribution with a mean of 172 cm and a standard deviation of 27 cm. In a particularly snowy year, the town recorded 226 cm of snow. Approximately what percentage of years would be expected to have snowfall amounts greater than 226 cm? Use the 68-95-99.7 rule to determine your answer.
3. Emma is analyzing the annual salaries of employees at a mid-sized technology firm. The salaries follow a normal distribution with a mean of $63,000 and a standard deviation of $9,000. The company's CEO announces that any employee whose salary is at or above the 84th percentile will receive a special bonus. Using the 68-95-99.7 rule, what is the minimum salary an employee must earn to qualify for the bonus?

…and 3 more problems