This lesson includes 25 additional questions and 243 additional question variations for subscribers.

# Lesson Worksheet: Applications of Normal Distribution Mathematics

In this worksheet, we will practice applying the normal distribution in real-life situations.

**Q1: **

A crop of apples has a mean weight of 105 g and a standard deviation of 3 g. It is assumed that a normal distribution is an appropriate model for this data. What is the approximate probability that a randomly selected apple from the crop has a weight less than 105 g?

**Q2: **

The monthly salaries of workers at a factory are normally distributed with mean 210 pounds and standard deviation 10 pounds. Determine the probability of choosing at random a worker with a salary between 184 and 233 pounds.

**Q3: **

In a school, the weights of students are normally distributed with mean 61 kg and standard deviation 8 kg. What percentage of students weigh between 50.6 kg and 61.64 kg?

**Q4: **

A crop of apples has a mean weight of 105 g and a standard deviation of 3 g. It is assumed that a normal distribution is an appropriate model for this data. What is the approximate probability that a randomly selected apple from the crop has a weight between 99 g and 111 g?

**Q5: **

A crop of apples has a mean weight of 105 g and a standard deviation of 3 g. It is assumed that a normal distribution is an appropriate model for this data. What is the approximate probability that a randomly selected apple from the crop has a weight between 102 g and 108 g?

**Q6: **

The masses of a population of blackbirds are normally distributed with mean 103 g and standard deviation 11 g.

To the nearest integer, what percentage of blackbirds have masses less than 110 g?

To the nearest tenth, what percentage of blackbirds have masses greater than 124 g?

To the nearest integer, what percentage of blackbirds have masses between 95 g and 120 g?

**Q7: **

In a school with 1,000 students, the heights of students are normally distributed with mean 113 cm and standard deviation 5 cm. How many students are shorter than 121 cm?

**Q8: **

The heights of a group of students follow a normal distribution with a standard deviation of 20 cm. The probability that a studentโs height is less than or equal to 180 cm is equal to the probability that a standard normal variable is less than or equal to 2.2. Find the mean height of the group of students.

**Q9: **

The heights of a sample of flowers are normally distributed with mean and standard deviation 12 cm. Given that of the flowers are shorter than 47 cm, determine .

**Q10: **

The monthly salaries of workers at a factory are normally distributed with mean and standard deviation 200 pounds. Given that of the workers earn more than 1,851 LE, find .