Worksheet 4

.pdf

School

University Of Connecticut *

*We aren’t endorsed by this school

Course

2500

Subject

Industrial Engineering

Date

Apr 3, 2024

Type

pdf

Pages

2

Uploaded by ChancellorElectron13476 on coursehero.com

Normal Probability Worksheet Name: Zachary Demanche Section: 035D 1. A sample of temperatures from a dolphin pool at Mystic Aquarium was found to be normally distributed with a mean of 72.4 degrees (F) and a standard deviation of 2.6 degrees (F). Represent the data with a normal curve and label the horizontal axis in standard deviation units. Then use the Empirical Rule to fill in the areas. Approximately what percentage of the time are the temperatures in the pool a. greater than 75 degrees? P (x>75) = 0.16 b. below 67.2 degrees? p(x<67.2) = 2.5% or 0.025 c. Between 67.2 and 77.6 degrees? p(67.2 <x<77.6) = 95% or 0.95 d. Between 67.2 and 75 degrees? p(76.2 <x< 75) = 47.5% + 34% = 81.5% or 0.85 e. Above 76 degrees? (You can only guess at this one!!) 6.5% f. If a temperature above 77.6 is unacceptable (too warm), what percent of the time is the temperature too warm? p(x>77.6) = 2.5% 2. For each example, draw the curve, shade the are you want to find, and use your calculator to find the area: 1. Between 95 and 267 for the normal random variable, X, with µ = 100 and s= 90. 0.490 2. Greater than 200 for the normal random variable, X, with µ = 100 and s= 90. 0.133 3. For each of the following examples, draw the curve, shade the area and find the corresponding value. 1. Find the number x such that the proportion of observations that are less than x in a normal curve with µ = 20 and s = 5 is 0.55. X = 20.63
2. Find the number x such that the proportion of observations that are greater than x in a normal curve with µ = 20 and s = 5 is 0.75. X = 16.63 3. Find the two x-values that mark off the middle 50% for a normal random variable with µ = 50 and s = 8. X1 = 44.60 X2 = 55.4 4. Find the two x-values that mark off the middle 80% for a normal random variable with µ = 100 and s = 16. X1 = 79.5 X2 = 120.5 4. The level of cholesterol in the blood is important because high cholesterol levels may increase the risk of heart disease. The distribution of blood cholesterol levels in a large population of people of the same age and sex is roughly Normal. For 14-year-old boys, the mean is 170 mgs. of cholesterol per deciliter of blood and the standard deviation is 30 mg/dl. Levels above 240 may require medical attention. What percent of 14-year-old boys have more than 240 mg/dl of cholesterol? 0.00981 or 0.98% 5. The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with mean 266 days and standard deviation 16 days. 1. What percent of pregnancies last less than 240 days (that’s about 8 months)? 0.052 or 5.2% 2. What percent of pregnancies last between 240 and 270 days? 0.547 or 54.7% 3. How long do the longest 20% of pregnancies last? X = 279.27 6. Find the x-values for the first and third quartiles of the distribution. Q1 = 255.21 Q2 = 276.79
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help