Step 2 - Greer Middle College || Building the Future

Get out your Standard Normal WS!

Today’s Objectives: You will be able to use a four-step method to solve Normal distribution problems.

Warm Up Use Table A to answer the following questions. 1. 𝑧 is between -1.24 and -0.32 Use Table A to answer the following questions. In each case sketch a standard Normal curve with your value of 𝒛 marked on the axis. 2. The 63rd percentile of the standard Normal distribution. 3. 75% of all observations are greater than 𝑧.

Homework Check

Homework Check

Normal Distribution Calculations Steps to find a percentile in problems involving Normal distributions. Step 1: State the problem in terms of the observed variable 𝑥. Step 2: Standardize and draw a picture. Step 3: Use the table. Step 4: Write your conclusion in the context of the problem.

Normal Method Example When Tiger Woods hits his driver, the distance the ball travels follows a Normal distribution with mean 304 yards and standard deviation 8 yards. What percent of Tiger’s drives travel at least 290 yards?

Step 1: State the problem Let 𝑥 = 𝜇 = 𝜎 = We want the proportion of drives with 𝑥 ≥ ____________.

Step 2: Standardize What is the 𝑧-score of 290?

Step 3: Use Table A Find the proportion of observations less than (to the left of) -1.75 and then find the area to the right to answer the question. Convert this decimal to a percent.

Step 4: Conclusion

About _______% of Tiger Woods’ drives on the range travel at least 290 yards.

Tiger Example Part 2 What percent of Tiger’s drive travel between 305 and 325 yards? Follow the four-step method.

Table A—In Reverse Steps to find a variable (x) in problems involving Normal distributions where the percentile is given.

Step 1: State the problem and draw a picture Step 2: Use Table A

Step 3: “Un-standardize” Step 4: Conclusion

Reverse Example When Tiger hits his driver, the distance the ball travels follows a Normal distribution with mean 304 yards and standard deviation 8 yards. What distance would a ball have to travel to be at the 80th percentile of Tiger’s drive lengths?

Step 1: State and Draw Let 𝜇 = 𝜎 = We want to find the drive distance 𝑥.

Step 2: Table A Look in Table A for the entry closest to 0.80.

Step 3: “Un-Standardize”

𝑥−𝜇 𝑧= 𝜎

Step 4: Conclusion A golf ball would have to travel ____________ yards to be at the 80th percentile of Tiger’s drive length distribution.

Running a Mile—Try One! During World War II, physical training was required for male students in many colleges, as preparation for military service. A study of 12,000 able-bodied male students at the University of Illinois found that their times for the mile run had mean 7.11 minutes and standard deviation 0.739 minutes. The distribution of times was roughly Normal.

Try One! Here are some sample questions one might ask about this distribution of times. Follow the four-step method to answer these questions. a) About how many of the 12,000 male students ran a mile in less than 5 minutes? b) What is the 93rd percentile in the mile run time distribution? c) Do you think students today could match this performance? Justify your answer.

Ticket Out The Door Write down the four-step method using Table A when finding a percentile. Then, Write down the four-step method using Table A in reverse when finding an unknown variable.

Homework

Four-Step Method Worksheet Due Friday