MATH 225N Week 5 Assignment: Applications of the Normal Distribution – Excel

1. Question: Sugar canes have lengths, X, that are normally distributed with mean 45centimeters and standard deviation 4.9centimeters. What is the probability of the length of a randomly selected cane being between 360and 370centimeters? Round your answer to four decimal places.
2. Question: The number of miles a motorcycle, X, will travel on one gallon of gasoline is modeled by a normal distribution with mean 44 and standard deviation 5. If Mike starts a journey with one gallon of gasoline in the motorcycle, find the probability that, without refueling, he can travel more than 50
3. Question: A worn, poorly set-up machine is observed to produce components whose length X follows a normal distribution with mean 14 centimeters and variance 9. Calculate the probability that a component is at least 12 centimeters long.
4. Question: The average speed of a car on the highway is 85 kmph with a standard deviation of 5 Assume the speed of the car, X, is normally distributed. Find the probability that the speed is less than 80 kmph.
5. Question: The time, X minutes, taken by Tim to install a satellite dish is assumed to be a normal random variable with mean 127 and standard deviation 20. Determine the probability that Tim will takes less than 150 minutes to install a satellite dish.
6. Question: The average number of acres burned by forest and range fires in a county is 4,500 acres per year, with a standard deviation of 780 The distribution of the number of acres burned is normal. What is the probability that between 3,000 and 4,800 acres will be burned in any given year? Round your answer to four decimal places.
7. Question: Suppose that the weight, X, in pounds, of a 40-year-old man is a normal random variable with mean 147 and standard deviation 16. Calculate P(X<185).
8. Question: Suppose that the weight, X , in pounds, of a 40 -year-old man is a normal random variable with mean 147 and standard deviation 16 . Calculate P(120≤X≤153) .
9. Question: A worn, poorly set-up machine is observed to produce components whose length Xfollows a normal distribution with mean 14centimeters and standard deviation 3 Calculate the probability that the length of a component lies between 19and 21centimeters.
10. Question: A firm’s marketing manager believes that total sales for next year will follow the normal distribution, with a mean of $3.2 million and a standard deviation of $250,000. Determine the sales level that has only a 3% chance of being exceeded next year.
11. Question: Suppose that the weight of navel oranges is normally distributed with a mean of μ=6 ounces and a standard deviation of σ=0.8 ounces. Find the weight below that one can find the lightest 90% of all navel oranges.
12. Question: A tire company finds the lifespan for one brand of its tires is normally distributed with a mean of 47,500 miles and a standard deviation of 3,000 miles. What mileage would correspond to the the highest 3% of the tires?
13. Question: The average credit card debt owed by Americans is $6375, with a standard deviation of $1200. Suppose a random sample of 36 Americans is selected. Identify each of the following:
14. Question: The heights of all basketball players are normally distributed with a mean of 72 inches and a population standard deviation of 1.5 inches. If a sample of 15 players are selected at random from the population, select the expected mean of the sampling distribution and the standard deviation of the sampling distribution below.
15. Question: After collecting the data, Peter finds that the standardized test scores of the students in a school are normally distributed with mean 85 points and standard deviation 3 points. Use the Empirical Rule to find the probability that a randomly selected student’s score is greater than 76 points. Provide the final answer as a percent rounded to two decimal places.
16. Question: After collecting the data, Christopher finds that the total snowfall per year in Reamstown is normally distributed with mean 94 inches and standard deviation 14 inches. Which of the following gives the probability that in a randomly selected year, the snowfall was greater than 52 inches? Use the empirical rule
17. Question: The College Board conducted research studies to estimate the mean SAT score in 2016 and its standard deviation. The estimated mean was 1020 points out of 1600 possible points, and the estimated standard deviation was 192 points. Assume SAT scores follow a normal distribution. Using the Empirical Rule, about 95% of the scores lie between which two values?
18. Question: After collecting the data, Kenneth finds that the body weights of the forty students in a class are normally distributed with mean 140 pounds and standard deviation 9 pounds. Use the Empirical Rule to find the probability that a randomly selected student has a body weight of greater than 113 pounds. Provide the final answer as a percent rounded to two decimal places.
19. Question: Miller’s science test scores are normally distributed with a mean score of 77 (μ) and a standard deviation of 3 (σ). Using the Empirical Rule, about 68% of the scores lie between which two values?
20. Question: Brenda has collected data to find that the finishing times for cyclists in a race has a normal distribution. What is the probability that a randomly selected race participant had a finishing time of greater than 154 minutes if the mean is 143 minutes and the standard deviation is 11 minutes? Use the empirical rule.
21. Question: Suppose X∼N(20,2), and x=26. Find and interpret the z-score of the standardized normal random variable.
22. Question: Isabella averages 17 points per basketball game with a standard deviation of 4 points. Suppose Isabella’s points per basketball game are normally distributed. Let X= the number of points per basketball game. Then X∼N(17,4).
23. Question: Suppose X∼N(6.5,1.5), and x=3.5. Find and interpret the z-score of the standardized normal random variable.
24. Question: Suppose X∼N(5.5,2), and x=7.5. Find and interpret the z-score of the standardized normal random variable.
25. Question: Jerome averages 16 points a game with a standard deviation of 4 points. Suppose Jerome’s points per game are normally distributed. Let X = the number of points per game. Then X∼N(16,4).
26. Question: Josslyn was told that her score on an aptitude test was 3 standard deviations above the mean. If test scores were approximately normal with μ=79 and σ=9, what was Josslyn’s score? Do not include units in your answer. For example, if you found that the score was 79 points, you would enter 79.
27. Question: Marc’s points per game of bowling are normally distributed with a standard deviation of 13 points. If Marc scores 231 points, and the z-score of this value is 4, then what is his mean points in a game? Do not include the units in your answer. For example, if you found that the mean is 150 points, you would enter 150.
28. Question: Floretta’s points per basketball game are normally distributed with a standard deviation of 4 points. If Floretta scores 10 points, and the z-score of this value is −4, then what is her mean points in a game? Do not include the units in your answer. For example, if you found that the mean is 33 points, you would enter 33.
29. Question: Jamie was told that her score on an aptitude test was 3 standard deviations below the mean. If test scores were approximately normal with μ=94 and σ=6, what was Jamie’s score? Do not include units in your answer. For example, if you found that the score was 94 points, you would enter 94.
30. Question: A normal distribution is observed from the number of points per game for a certain basketball player. If the mean is 16 points and the standard deviation is 2 points, what is the probability that in a randomly selected game, the player scored between 12 and 20 points? Use the empirical rule
31. Question: A random sample of vehicle mileage expectancies has a sample mean of x¯=169,200 miles and sample standard deviation of s=19,400 miles. Use the Empirical Rule to estimate the percentage of vehicle mileage expectancies that are more than 188,600 miles.
32. Question: A random sample of lobster tail lengths has a sample mean of x¯=4.7 inches and sample standard deviation of s=0.4 inches. Use the Empirical Rule to determine the approximate percentage of lobster tail lengths that lie between 4.3 and 5.1 inches.
33. Question: A random sample of SAT scores has a sample mean of x¯=1060 and sample standard deviation of s=195. Use the Empirical Rule to estimate the approximate percentage of SAT scores that are less than 865.
34. Question: The number of pages per book on a bookshelf is normally distributed with mean 248 pages and standard deviation 21 pages. Using the empirical rule, what is the probability that a randomly selected book has less than 206 pages?
35. Question: Karly’s math test scores are normally distributed with a mean score of 87 (μ) and a standard deviation of 4 (σ). Using the Empirical Rule, about 99.7% of the data values lie between which two values?
36. Question: In 2014, the CDC estimated that the mean height for adult women in the U.S. was 64 inches with a standard deviation of 4 inches. Suppose X, height in inches of adult women, follows a normal distribution. Which of the following gives the probability that a randomly selected woman has a height of greater than 68 inches?
37. Question: A normal distribution is observed from the number of points per game for a certain basketball player. The mean for this distribution is 20 points and the standard deviation is 3 points. Use the empirical rule for normal distributions to estimate the probability that in a randomly selected game the player scored less than 26 points.
38. Question: A normal distribution is observed from the number of points per game for a certain basketball player. If the mean is 15 points and the standard deviation is 3 points, what is the probability that in a randomly selected game, the player scored greater than 24 points? Use the empirical rule
39. Question: The College Board conducted research studies to estimate the mean SAT score in 2016 and its standard deviation. The estimated mean was 1020 points out of 1600 possible points, and the estimated standard deviation was 192 points. Assume SAT scores follow a normal distribution. Using the Empirical Rule, about 95% of the scores lie between which two values?
40. Question: The typing speeds for the students in a typing class is normally distributed with mean 44 words per minute and standard deviation 6 words per minute. What is the probability that a randomly selected student has a typing speed of less than 38 words per minute? Use the empirical rule
41. Question: Nick has collected data to find that the body weights of the forty students in a class has a normal distribution. What is the probability that a randomly selected student has a body weight of greater than 169 pounds if the mean is 142 pounds and the standard deviation is 9 pounds? Use the empirical rule.
42. Question: The times to complete an obstacle course is normally distributed with mean 73 seconds and standard deviation 9 seconds. What is the probability using the Empirical Rule that a randomly selected finishing time is less than 100 seconds?
43. Question: After collecting the data, Douglas finds that the finishing times for cyclists in a race is normally distributed with mean 149 minutes and standard deviation 16 minutes. What is the probability that a randomly selected race participant had a finishing time of less than 165 minutes? Use the empirical rule
44. Question: Charles has collected data to find that the total snowfall per year in Reamstown has a normal distribution. Using the Empirical Rule, what is the probability that in a randomly selected year, the snowfall was less than 87 inches if the mean is 72 inches and the standard deviation is 15 inches?
45. Question: Christopher has collected data to find that the total snowfall per year in Laytonville has a normal distribution. What is the probability that in a randomly selected year, the snowfall was greater than 53 inches if the mean is 92 inches and the standard deviation is 13 inches? Use the empirical rule
46. Question: The times to complete an obstacle course is normally distributed with mean 87 seconds and standard deviation 7 seconds. What is the probability that a randomly selected finishing time is greater than 80 seconds? Use the empirical rule
47. Question: Sugar canes have lengths, X, that are normally distributed with mean 45centimeters and standard deviation 4.9centimeters. What is the probability of the length of a randomly selected cane being between 360 and 370 centimeters?
48. Question: On average, 28percent of 18 to 34 year olds check their social media profiles before getting out of bed in the morning. Suppose this percentage follows a normal distribution with a random variable X, which has a standard deviation of five percent. Find the probability that the percent of 18 to 34 year olds who check social media before getting out of bed in the morning is, at most, 32.
49. Question: In a survey of men aged 20-29in a country, the mean height was 4 inches with a standard deviation of 2.7 inches. Find the minimum height in the top 10% of heights.
50. Question: Two thousand students took an exam. The scores on the exam have an approximate normal distribution with a mean of μ=81points and a standard deviation of σ=4 The middle 50% of the exam scores are between what two values?
    

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Further Questions-Answers

1. Question: Sugar canes have lengths, X, that are normally distributed with mean 45centimeters and standard deviation 4.9centimeters. What is the probability of the length of a randomly … between 360 and 370 centimeters?
2. Question: On average, 28percent of 18 to 34 yearolds check their social media profiles before getting out of bed in the morning. Suppose this percentage follows a normal distribution with a random variable X, which has a standard deviation of five percent. Find the probability that the percent of 18 to 34 yearolds who check social media before getting out of bed in the morning is, at most, 32.
3. Question: In a survey of men aged 20-29in a country, the mean height was 4 inches with a standard deviation of 2.7 inches. Find the minimum height in the top 10% of heights.
4. Question: Two thousand students took an exam. The scores on the exam have an approximate normal distribution with a mean of μ=81points and a standard deviation of σ=4 The middle 50% of the exam scores are between what two values?