Normal Distribution Worksheets Grade 11

1. Hana is analyzing the distribution of the weights of a rare species of fish in a lake. The weights are normally distributed with a mean of 28 kg and a standard deviation of 5 kg. A normal distribution curve is drawn with the mean at 28 kg. Shade the region on the curve that represents fish weighing between 18 kg and 38 kg. Using the 68-95-99.7 rule, approximately what percentage of the fish fall in this shaded region?
2. Hana is a botanist studying the heights of a particular species of tree in a forest reserve. The heights follow a normal distribution with a mean of 12.4 meters and a standard deviation of 2.1 meters. Hana selects a tree at random. What is the probability, expressed as a percentage, that the tree's height is between 10.3 meters and 14.5 meters? Use the 68-95-99.7 rule (empirical rule) to approximate your answer.
3. Tane is analyzing the battery life of a new smartphone model. The battery life follows a normal distribution with a mean of 48 hours and a standard deviation of 6 hours. The manufacturer guarantees that the battery will last at least 36 hours. What percentage of smartphones are expected to have a battery life less than the guaranteed minimum of 36 hours?

…and 3 more problems

1. 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?
2. Normal: μ=72, σ=9. What % between 54 and 90?
3. Noah is analyzing the weights of adult male African elephants in a reserve. The weights follow a normal distribution with a mean of 5000 kg and a standard deviation of 400 kg. Using the 68-95-99.7 rule, what percentage of these elephants weigh between 4200 kg and 5800 kg?

…and 4 more problems

1. Aroha is studying the distribution of test scores from a large Grade 11 mathematics competition. The scores are normally distributed with a mean of 52 points and a standard deviation of 9 points. On a normal distribution curve, shade the region that represents scores between 43 and 70 points. Using the 68-95-99.7 rule, approximately what percentage of all scores fall in this shaded region?
2. A factory produces precision components with lengths that follow a normal distribution. The quality control manager, Liam, finds that 15% of components are shorter than 48.2 mm and 20% are longer than 51.4 mm. Calculate the mean and standard deviation of the component lengths.
3. Hana is a botanist studying the height of a particular species of sunflower. She finds that the heights follow a normal distribution with a mean of 210 cm and a standard deviation of 15 cm. Using the 68-95-99.7 rule, what percentage of sunflowers are expected to be taller than 240 cm?

…and 3 more problems