Z ScoreQuiz Review IP

1. Label the normal distribution model with the Empirical Rule percentages.

2. The lifespans oflionsin a particular zoo are normally distributed. The average lion lives 11 years; the standard deviation is 1.6 years.

  1. Shade the region of lions living between 6.2 and 15.8 years.
  1. What percentage of lions live between 6.2 and 15.8 years?

3. The graph summarizes the test scores of 10000 students. The data is normally distributed with a mean of 72 and a standard deviation of 4.

Shade the regions under the curve where only the data for approximately 1585 above average scores are located.

  1. a. You score 680 on the mathematics portion of the SAT. If the math scores on the

SAT are normally distributed with μ = 518 and σ = 114, find your z-score.

  1. You score 27 on the ACT assessment mathematics test. If the ACT math scores are normally distributed with mean 20.7 and standard deviation 5.0, find your friends’ z-score.
  1. On which test did you get the better score? Why?
  1. Students who drive to school are randomly selected. Each participant is asked the travel time (in minutes) it takes to drive from their home, park the car, and enter the school. After analyzing the data, it is determined that the data is normally distributed with a mean of 20 minutes and a standard deviation of 3 minutes.
  2. If the travel time is 26 minutes, determine the corresponding z-score.
  1. What travel time corresponds to a z-score of-2.67?
  1. Professor Halen has 184 students in her college mathematics lecture class. The scores on the midterm exam are normally distributed with a mean of 72.3 and a standard deviation of 8.9. What percent of students in the class can be expected to receive a score between 82 and 90? How many students is this? Round your answer to the nearest student.
  1. A group of 625 students has a mean age of 15.8 years with a standard deviation of 0.6 years. The ages are normally distributed. What percent of students are younger than 16.2 years? Approximately how many students are younger than 16.2 years? Express answer to the nearest student.
  1. The heights of a group of people make a normal distribution with a mean of 65 inches and a standard deviation of 5 inches.
  2. What height falls in the 47th percentile?b. What height falls in the 65th percentile?

Answer Bank:

1.26 / 64.65 inches / 11.46% / 1.42 / 74.86%
468 students / 99.7% / 21 students / 66.95 inches / 11.99 minutes
2 / SAT, higher z-score

Have a teacher check your shading and labels for #1-3