Given that the heights of males ages 18-25 (measured in inches) have the distribution N(69.5, 1.5), find each of the following. This notation means that it follows a normal curve, their mean height is 69.5 inches, and their standard deviation is 1.5 inches. Draw a normal curve first and use that to answer the questions. Make sure that you label the x-axis correctly. You will need to find z-scores to answer each of these questions. 1. How tall would an 18 to 25 male have to be in order to be in the 73rd percentile? 2. What proportion of males 18 to 25 are between 68 and 71 inches tall? 3. If a 20-year- old make is 73 inches tall, what percentile would this place him? 4. What is the probability that a randomly selected male (age 18 to 25) is less than 67 inches tall or over 72 inches tall? 5. What can we infer about a man 18 to 25 that is 66 inches tall?
Added by Stephanie H.
Close
Step 1
To find the height that corresponds to the 73rd percentile, we need to find the z-score that corresponds to this percentile. Using a standard normal distribution table, we find that the z-score for the 73rd percentile is approximately 0.61. We then use the formula Show moreā¦
Show all steps
Your feedback will help us improve your experience
Joanna Quigley and 85 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Ahmet Y.
Men's heights are normally distributed with a mean of 69 inches and a standard deviation of 3 inches. Use this information to answer the following questions. Show all of your work for full credit. 1. What is the probability of selecting a man who is taller than 71 inches? 2. What is the probability of selecting a man who is shorter than 67 inches? 3. What is the probability of selecting a man who is taller than 64 inches and shorter than 68 inches? SAT scores are normally distributed with a mean of 500 points and a standard deviation of 100 points. Use this information to answer the following questions. Show all your work for full credit. 4. What is the probability of selecting a student that scored above 650? 5. What score represents the score at the 90th percentile?
The heights of 18-year-old men are approximately normally distributed with mean of 68 inches and standard deviation of 3 inches. PART 1: What is the probability that an 18-year-old man selected at random is between 67 and 71 inches tall? Round to 4 decimal places. PART 2: For a sample of 36 18-year-old men, what is the probability that the average of their heights is between 67 and 71 inches? Round to 4 decimal places. PART 3: What sample n would be necessary in order to have P(67 < xĢ < 69) = 0.95 Round to the nearest whole number.
T. L.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Watch the video solution with this free unlock.
EMAIL
PASSWORD