MSIS 111 PROBABILITY EXCEL

MSIS 111L Chapter 6: Continuous Distributions

Calculator and Excel Lab

Homework Assignment Questions

Instructions:

1. Answer all lab questions highlighted in yellow.

2. Answer Cengage Homework Questions # 7, 8 & 9. Provide Solutions in both 1. Excel and 2. Using your TI

Calculator

Please label your Excel Tabs so the TI and the Excel questions are in separate tabs

Submission: Submit via the Blackboard Assignment Tab.

LAB TUTORIAL

The Normal Probability Distribution menu for the TI83+/84+ is found under 2nd/VARS

NOTE: A mean of zero and a standard deviation of one are considered to be the default values for a normal distribution

on the calculator, if you choose not to set these values.

The Normal Distribution functions: If you need additional support, Watch YouTube Videos on Blackboard

#1: normalpdf = Probability Density Function This function returns the probability of a single value of the random variable x. Use

this to graph a normal curve. Using this function returns the y-coordinates of the normal curve. Syntax: normalpdf (x, mean,

standard deviation)

#2: normalcdf = Cumulative Distribution Function Theoretically, This function returns the cumulative probability from zero up to

some input value of the random variable x. Technically, it returns the percentage of area under a continuous distribution curve from

negative infinity to the x. You can, however, set the lower bound. Syntax: normalcdf (lower bound, upper bound, mean, standard

deviation)

#3: invNorm = Inverse Normal Probability Distribution Function This function returns the x-value given the probability region to the

left of the x-value. (0 < area < 1 must be true.) The inverse normal probability distribution function will find the precise value at a

given percent based upon the mean and standard deviation. Syntax: invNorm (probability, mean, standard deviation)

Z Score Formula: Standardized Normal Distribution

, 0 x

z 

  

 

A z score is the number of standard deviations that a value, x, is above or below the mean. The z distribution is a normal

distribution with a mean of 0 and a standard deviation of 1.

Demonstration Problem: Part A

Note: This is for your review only. Questions and Instruction’s posted at the end of the Lab.

Using data from the waste generation example, if a U.S. person is randomly selected, what is the probability that the

person generates between 3.60 and 5.00 pounds of waste? For this example µ = 4.43 and σ = 1.32.

1. To compute probabilities from a normal distribution, go to an empty cell in an Excel worksheet and from the Insert Function (fx), select the Statistical category and the function NORM.DIST.

2. To calculate what percentage of values would lie between 2 values, you can subtract the probability to the left of the smaller value from the probability to the left of the larger value. You can do the calculations separately using the dialog box for NORM.DIST of you can use functions in one formula to calculate the in-between formula for the percentage:

= NORM.DIST(5.00,4.43,1.32,1)-NORM.DIST(3.60,4.43,1.32,1)

The in-between percentage would be 0.4023. Due to roundoff, the answer might slightly differ, as the

value of 0.4021 in the text.

Demonstration Part B: Note this is for your review only. Questions and Instructions posted at end of Lab.

Using data from the waste generation example, if a U.S. person is randomly selected, what is the probability that the

person generates between 5.30 and 6.50 pounds of waste? For this example µ = 4.43 and σ = 1.32.

1. To compute probabilities from a normal distribution, go to an empty cell in an Excel worksheet and from the Insert Function (fx), select the Statistical category and fill in the appropriate arguments for the function NORM.DIST and conduct the calculations in two separate steps subtracting the percentage of the smaller value from the percentage of the larger value.

2. You can also type the function into an empty cell: = NORM.DIST(6.50,4.43,1.32,1)-NORM.DIST(5.30,4.43,1.32,1)

The in-between percentage would be 0.1965. Due to roundoff, the answer might slightly differ, as the

value of 0.1964 in the text.

Demonstration Problem: Part C. Note this is for your review only. Questions and Instructions posted at end of Lab.

A particular ten inch (in diameter) clay pipe weighs, on average, 44 pounds, and pipe weights are normally distributed in

the population. If 74.22% of the pipe weights are more than 40 pounds, what is the value of the standard deviation? The

mean µ = 44. The value of x is 40. The standard deviation is unknown.

1. To calculate the unknown standard deviation, you can solve for it in the z formula.

Given the percentage to the right of 40 pounds, we can use a function in Excel to find what z value is

represented by that percentage. The Excel function NORM.S.INV calculates the z value for a given

probability to the left of a particular value. In the problem, we are given the percentage > 40 pounds,

so we need to subtract that value from 1 to get the percentage < 40 pounds.

2. We can then use the NORM.S.INV function to retrieve the z value for 25.78%. Use Insert Function fx to access the Statistical function NORM.S.INV. Input 0.2578 for the Probability. The resulting z-value is -0.65.

3. We can use the z value to solve for the unknown standard deviation. 40 44

0 65. 

  

40 44 z

 



Input the following formula in Excel: = (40-44)/(-0.65)

The answer is 6.154.

Homework Assignment Questions

Instructions: Answer questions #1 & 2 highlighted in yellow. Upon completion, answer questions #7, 8 & 9 in your

Cengage textbook.

 Refer to the former instructions to make the following normal probability deductions using your TI-Calculator.

Part I

Question #1

Given a normal distribution of values for which the mean is 70 and the standard deviation is 4.5.

A. Find the probability that a value is between 65 and 80, inclusive.

B. Find the probability that a value is greater than or equal to 75.

C. Find the probability that a value is less than 62.

D. Fine the 90th percentile for this distribution.

Part II

Answer Cengage Homework Questions # 7, 8 & 9

Label your Excel Tabs so the TI and the Excel questions are in separate tabs

Submission: Submit via the Blackboard Assignment Tab.