Z-Scores and Standard Deviation Worksheets Grade 10

1. A pharmaceutical company is testing a new medication and finds that the time it takes for patients to experience symptom relief follows a normal distribution with a mean of 45 minutes and a standard deviation of 8 minutes. If Liam takes this medication and experiences relief in 35 minutes, what is the z-score for his relief time?
2. Isabella is a quality control analyst at a juice bottling plant. The volume of juice in each bottle follows a normal distribution with a mean of 502 mL and a standard deviation of 3 mL. During a routine check, Isabella selects a bottle and finds it contains 511 mL of juice. Calculate the z-score for this bottle's volume and explain what it means.
3. Matiu is a botanist studying the growth of a rare tree species in a controlled environment. The heights of these trees after two years follow a normal distribution with a mean of 45 cm and a standard deviation of 8 cm. Matiu measures one particular tree and finds it to be 61 cm tall. What is the z-score for this tree's height, and what does it indicate?

…and 4 more problems

1. A pharmaceutical company is testing a new medication. The average blood pressure reduction in clinical trials is 12 mmHg with a standard deviation of 3 mmHg. If a patient experiences a reduction of 18 mmHg, what is their z-score?
2. A normal distribution of test scores has a mean of 75 and a standard deviation of 8. If a student scores 91 on the test, what is their z-score?
3. A normal distribution has μ = 82 and σ = 6. If x = 70, then z = ?

…and 5 more problems

1. A university is studying the heights of its basketball players. The team's heights follow a normal distribution with a mean of 192 cm and a standard deviation of 6 cm. If Noah, a player on the team, has a height of 204 cm, what is his z-score?
2. The heights of students in a Grade 10 class follow a normal distribution with a mean of 165 cm and a standard deviation of 6 cm. If a student is 178 cm tall, what is their z-score? Round your answer to two decimal places.
3. A box-and-whisker plot shows the distribution of test scores for a Grade 10 class. The mean score is 73 and the standard deviation is 9. Aroha's score is represented on the plot, and her z-score is 3. What is Aroha's actual test score?

…and 4 more problems