Z-Scores and Standard Deviation Worksheets Grade 10

1. 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?
2. Olivia is a marine biologist studying the lengths of adult sea otters in a protected coastal region. The lengths follow a normal distribution with a mean of 145 cm and a standard deviation of 7 cm. She measures one adult sea otter and finds its length to be 159 cm. What is the z-score for this otter's length, and what does it indicate about how this otter compares to the population?
3. Kaia is analyzing the germination times of a rare native plant species. The germination times (in days) follow a normal distribution with a mean of 21 days and a standard deviation of 3 days. One particular seed from Kaia's experiment germinated in 15 days. Calculate the z-score for this germination time and interpret what this value means in terms of standard deviations from the mean.

…and 5 more problems

1. Charlotte is studying the battery life of a new smartphone model. The battery life follows a normal distribution with a mean of 18 hours and a standard deviation of 3 hours. If one smartphone from the production line has a battery life of 24 hours, what is the z-score for this smartphone's battery life, and what does it indicate about its performance relative to the average?
2. Olivia is a botanist studying the germination times of a rare orchid species. The germination times follow a normal distribution with a mean of 25 days and a standard deviation of 5 days. One particular seed she is observing germinates in 35 days. What is the z-score for this germination time, and what does it indicate about how this seed compares to the average?
3. Sophia is training for a regional cross-country meet and has been tracking her running times. Her coach tells her that the times for all runners in her age group follow a normal distribution with a mean time of 28 minutes and a standard deviation of 4 minutes. If Sophia's personal best time is 22 minutes, what is her z-score and what does it indicate about her performance relative to other runners?

…and 4 more problems

1. A normal distribution has μ = 82 and σ = 6. If x = 94, then z = ?
2. z = (82 - 70) ÷ 4 = ?
3. A botanist measures the petal lengths of a rare flower species. The distribution of petal lengths is normal with a mean of 7.2 cm and a standard deviation of 1.7 cm. One particular flower, collected by Charlotte, has a petal length of 10.6 cm. Draw a normal distribution curve in your mind, place the mean at the center, and mark Charlotte's flower on the curve. What is the z-score for this flower's petal length, and what does it tell you about how its length compares to the rest of the population?

…and 4 more problems