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

See similar textbooks

Related questions

Concept explainers

Question

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

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Expert Solution

Step by step

Solved in 5 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Point Estimation, Limit Theorems, Approximations, and Bounds$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions