Name: Instructor: Date: Section: PRACTICE PROBLEMS 1. This table is a probability distribution in which x represents the number of students that a statistics tutor may see on any given day and P( x) represents the probability that the tutor sees that number of students. x P(x) 0 0.11 1 0.18 2 0.36 3 0.16 4 0.14 5 0.05 a. Confirm that this is a legitimate probability distribution by stating the conditions that must be satisfied and showing how they are satisfied. b. Find the mean and the standard deviation of this distribution. c. Based on this distribution, what is the probability that a tutor sees at least two students on a certain day? Copyright 5-9 2018 Pearson Education, Inc. Name: Instructor: 2. Date: Section: d. Based on this distribution, what is the probability that a tutor sees either three or four students on a certain day? e. Based on this distribution, what is the probability that a tutor sees exactly 10 students on a certain day? A recent survey by a car insurance company revealed that 80% of teenage girls text while driving. You have been hired to do a safety presentation to a high school class of 100 teenage girls. You will ask how many of them text while driving. a. Explain why this procedure results in a binomial distribution. b. State the values of n, p, and q for this distribution. Copyright 5-10 2018 Pearson Education, Inc. Name: Instructor: Date: Section: c. What is the mean number of girls in this class who text while driving? d. What is the expected number of girls in this class who text while driving? e. What is the standard deviation of this distribution? f. What is the probability that exactly 75 of these girls text while driving? g. What is the probability that at most 75 of these girls text while driving? h. What is the probability that at least 75 of these girls text while driving? Copyright 5-11 2018 Pearson Education, Inc. Section 6.2 – Real Applications of the Normal Distribution Name __________________________ FINDING A PERCENT/PROPORTION/AREA given an x value FINDING AN X VALUE given a percentage/proportion/area Standardize 𝑥 to restate the problem in terms of a 𝑥−𝜇 standard normal variable 𝑧 = 𝜎 . Draw a picture to show the area of interest under the standard normal curve. Then find the required area under the standard normal curve using the 𝑧-table. Look in the body of the 𝑧-table for the entry closest to the given proportion to find the corresponding 𝑧score. “Unstandardize” to transform the solution from a z-score to a value of 𝑥 using the equation 𝑥 = 𝑧𝜎 + 𝜇. • We can also complete these problems using • We can also complete these problems using technology. (Make sure to try both methods.) technology without the need to standardize values. Scores on the Wechsler Adult Intelligence Scale, a standard IQ test, are approximately normal for the 20 to 34 age group with µ = 110 and σ = 25. 1. What percent of this age group have an IQ less than 100? 2. What percent of this age group have an IQ between 90 and115? 3. Find the 80th percentile of the IQ scores distribution of 20 to 34 year olds. 4. Find the IQ score which separates the lowest 25% of all IQ scores for this age group from the highest 75%. The adult men of the Dinaric Alps have the highest average height of all regions. The distribution of height is approximately normal with a mean height of 6 ft 1 in (73 inches) and standard deviation of 3 inches. 5. Find the 40th percentile of the height of Dinaric Alps distribution for men. 6. What percentage of men have a height greater than 74 inches? 7. What percentage of men have a height between 70 inches and 78 inches? 8. The average height of adult American men is 69 inches. What percent of the adult men in the Dinaric Alps are taller than the average American man? 9. What would be the minimum height of man in the Dinaric Alps that would place him in the top 10% of all heights? The length of pregnancy for the Asian elephant has an approximately normal distribution with an average length of 609 days and standard deviation of 31 days. 10. How long do the longest 5% of all elephant pregnancies last? 11. What percent of the elephant pregnancies last between 600 and 615 days? 12. The shortest 20% of all elephant pregnancies last fewer than how many days? 13. The middle 50% of all elephant pregnancies fall between how many days?
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