Solve the following: Graph and write all the necessary solution, then, box your final answer. (5 points each) 1. The daily income of bank auditors in SSS Commercial Bank is normally distributed with a mean of 675 pesos and a standard deviation of 45 pesos. What is the z value for the income x of a bank auditor who earns 700 pesos daily? For an auditor who earns 450 pesos daily? 2. The length of time needed to service a motorcycle at ETS Service Station is normally distributed with mean 6.8 minutes and standard deviation of 1.2 minutes. What is the probability that a randomly selected motorcycle will require more than 7.2 minutes of service under 5.6 minutes of service? 3. The average price of a new two-story townhouse is 1,600,000 pesos, find the maximum and minimum prices of the townhouse that a contractor will build to include the middle 70% of the market. Assume that the standard deviation of prices is 300,000 pesos and the variable is normally distributed. 4. Consider that in a population of Filipino adults ages 18 to 65, Body Mass Index (BMI) is normally distributed with a mean of 28 and a standard deviation of 6. (a) What is the BMI mark of the bottom 20% of the distribution for this population? (b) What BMI marks the bottom 10% of the distribution for this population? 5. The heights of 1,000 college students are normally distributed about a mean value of 170 centimeters. The standard deviation is 7.2 centimeters. Find how many students are smaller than 158 centimeters.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Solve the following: Graph and write all the necessary solution, then, box your final answer. (5 points each) 1. The daily income of bank auditors in SSS Commercial Bank is normally distributed with a mean of 675 pesos and a standard deviation of 45 pesos. What is the z value for the income x of a bank auditor who earns 700 pesos daily? For an auditor who earns 450 pesos daily? 2. The length of time needed to service a motorcycle at ETS Service Station is normally distributed with mean 6.8 minutes and standard deviation of 1.2 minutes. What is the probability that a randomly selected motorcycle will require more than 7.2 minutes of service under 5.6 minutes of service? 3. The average price of a new two-story townhouse is 1,600,000 pesos, find the maximum and minimum prices of the townhouse that a contractor will build to include the middle 70% of the market. Assume that the standard deviation of prices is 300,000 pesos and the variable is normally distributed. 4. Consider that in a population of Filipino adults ages 18 to 65, Body Mass Index (BMI) is normally distributed with a mean of 28 and a standard deviation of 6. (a) What is the BMI mark of the bottom 20% of the distribution for this population? (b) What BMI marks the bottom 10% of the distribution for this population? 5. The heights of 1,000 college students are normally distributed about a mean value of 170 centimeters. The standard deviation is 7.2 centimeters. Find how many students are smaller than 158 centimeters.

Test B. Find the probabilities for each, using the standard normal distribution. (3 points each)
1. P (0 < z < 2.64)
3. P(z > 0.52)
-3
-2
-1
2
-3
-2
-1
2
3
2. Р(z> - 2.14)
4. Р(-2.73 <2<-0.73)
-3
-2
-1
-3
-2
-1
2
3

WORKSHEET 3: Normal Distribution
Test A: Find the area under the standard normal distribution curve. (3 points each)
1. Between z = 0 and z = 1.51
3. Between z = 0 and z = -2.03
-2
-1
2
3
-2
-1
1
2. To the right of z = 1.37
4. To the left of z = 2.05
-3
-1
1
3
-2
-1
3

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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