MATH 225N Week 5 Assignment: Applications of the Normal Distribution – Chamberlain College of Nursing | MATH225N Week 5 Assignment: Applications of the Normal Distribution – Winter 2019

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MATH 225N Week 5 Assignment: Applications of the Normal Distribution – Chamberlain College of Nursing Week 5 Assignment: Applications of the Normal Distribution Question Sugar canes have length... s, X , that are normally distributed with mean 365.45 centimeters and standard deviation 4.9 centimeters. What is the probability of the length of a randomly selected cane being between 360 and 370 centimeters?  • Round your answer to four decimal places. The mean is μ=365.45 , and the standard deviation is σ=4.9 . As the probability between two values is to be calculated, subtract the probability of the lower value from the higher value. In this case, you have to use the NORMDIST function twice. 1. Open Excel and click on any empty cell. Click Insert function, fx . 2. Search for NORMDIST in the search for a function dialog box and click GO. 3. Make sure NORMDIST is on top in select a function. Then click OK. 4. In the function arguments of NORMDIST function, enter 370 for X , 365.45 for Mean, 4.9 for Standard_dev, and TRUE for Cumulative, all for the higher value of X . Thus, the answer, rounded to four decimal places, is 0.8234 . 5. Click on any other empty cell. Click Insert function, fx . 6. Search for NORMDIST in the search for a function dialog box and click GO. 7. Make sure NORMDIST is on top in select a function. Then click OK. 8. In the function arguments of NORMDIST function, enter 360 for X , 365.45 for Mean, 4.9 for Standard_dev, and TRUE for Cumulative, all for the lower value of X . Thus, the answer, rounded to four decimal places, is 0.1330 . Now subtract, 0.8234−0.1330=0.6904 . Thus, the probability of the length of a randomly selected cane being between 360 and 370 centimeters is 0.6904 . 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 miles.  • Round your answer to four decimal places. The mean is μ=44, and the standard deviation is σ=5. The probability that Mike can travel, without refueling, more than 50 miles is shown below.   A normal curve is over a horizontal axis and is divided into 3 regions. Vertical line segments extend from the horizontal axis to the curve at the mean, 44 and at 50. The right region is shaded.   First find the probability to the left of 50 and subtract from 1. 1. Open Excel and click on any empty cell. Click Insert function, fx. 2. Search for NORMDIST in the search for a function dialog box and click GO. 3. Make sure NORMDIST is on top in select a function. Then click OK. 4. In the function arguments of NORMDIST function, enter 50 for X, 44 for Mean, 5 for Standard_dev, and TRUE for Cumulative. This probability, rounded to four decimal places, is 0.8849. Now subtract, 1−0.8849=0.1151. Thus, the desired probability is P(X>50)=0.1151. 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. • Round your answer to four decimal places. The mean is μ=14, and the standard deviation is σ=9–√=3. 1. Open Excel and click on any empty cell. Click Insert function, fx. 2. Search for NORMDIST in the search for a function dialog box and click GO. 3. Make sure NORMDIST is on top in select a function. Then click OK. - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 1. On average, 28 percent 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.  • Round your answer to four decimal places. .7881 • The mean is μ=28, and the standard deviation is σ=5. • 1. Open Excel and click on any empty cell. Click Insert function, fx. • 2. Search for NORMDIST in the search for a function dialog box and click GO. • 3. Make sure NORMDIST is on top in select a function. Then click OK. • 4. In the function arguments of the NORMDIST function, enter 32 for X, 28 for Mean, 5 for Standard_dev, and TRUE for Cumulative. • Thus, the answer, rounded to four decimal places, is P(X<32)≈0.7881. 2. In a survey of men aged 20-29 in a country, the mean height was 73.4 inches with a standard deviation of 2.7 inches. Find the minimum height in the top 10% of heights.  • Use Excel, and round your answer to one decimal place. 76.9 3. Two thousand students took an exam. The scores on the exam have an approximate normal distribution with a mean of μ=81 points and a standard deviation of σ=4 points. The middle 50% of the exam scores are between what two values? • Use Excel, and round your answers to the nearest integer. 78-84 [Show More]

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