Stat121 Lesson 10

In order to find the z-score with 40% of the area to its left, what cumulative area should you look up?

0.4000

In order to find the z-scores with middle area of 60% symmetric about µ = 0, what cumulative area should you look up?

100% - 60% = 40%; dividing 40% by 2 to get the area in the lower tail, we get 20% or 0.2000.

A z-score of -0.67 has 25% of the area less than it and 75% of the area greater than it. What do we call this value?

Q1

To find area on the left for a z-score using the Standard Normal table, what should one do?

Simply look up the z-score

How do you find area to the right of a z-score using a cumulative proportion?

Subtract the cumulative area for the z-score from 1.0.

What part of a z-score is given by the values in the top row of a Standard Normal curve?

The top row gives the hundreths digit for a z-score.

Why is drawing the Normal curve and shading the desired area important?

To know whether you want area on the left, on the right or between two x-values.

True or false: Areas given by the Standard Normal Table are cumulative proportions.

True

True or false: When finding an x-value for a given area, you should find the z-score corresponding to the area in the Standard Normal table and use x = µ + zσ to find the x-value.

True

True or false: Before finding a z-score for a given area, you should always convert the given area to a cumulative area if it is not already a cumulative area.

True.

True or false: The Standard Normal table gives both areas to the right and areas to the left.

false. The Standard Normal table gives only cumulative areas which are areas to the left.

What is the first step in finding an area under a Normal distribution for an x-value using the Standard Normal table?

Compute the z-score for the x-value.

To find area between two z-scores using the Standard Normal table, what should one do?

Look up both z-scores and subtract the smallest cumulative area from the largest.

To find area on the right for a z-score using the Standard Normal table, what should one do?

Look up the z-score and subtract the corresponding cumulative area from 1.0.

Math SAT scores are Normally distributed with mean µ = 500 and standard deviation σ = 100. Using the 68-95-99.7 rule, what can you say about the area for the proportion of students who score between 325 and 375 on the SAT Math test? (No work necessary.)

16% of the area is less than 400 and 2.5% is less than 300. So, the area is between 16% and 2.5%. Further, it should be less than 13.5% since 13.5% of the area is between 300 and 400.

In order to find the z-score with 90% of the area to its right, what cumulative area should you look up?

90% is area on the right. To get cumulative area, we subtract 90% from 100% to get 10% or 0.1000

When given a cumulative proportion and asked for the corresponding z-score, how do we use the Standard Normal Table?

Look for the cumulative proportion in the center of the table and read the z-score in the margins.

Where do we locate a proportion (area) in the Standard Normal table?

Cumulative areas (proportions) are given in the inside of the Standard Normal table.

Question 1. Which of the following is a way to find areas other than 68-95-99.7 for a Normal distribution? A. Iterate using the 68-95-99.7 numbers B. Use the Standard Normal table C. Use statistical software D. Both A and B E. Both A and C F. Both B and C

F. Both B and C. We use either the Standard Normal table or statistical software to find areas for a Normal distribution.

True or false: You can only use the Standard Normal table to find cumulative proportions.

False. You can use the Standard Normal table in two ways: (1) to find a cumulative proportion for a z-score and (2) to find a z-score for a cumulative proportion

True or false: To find a z-score in the Standard Normal table, just look up the given proportion inside the table and read the z-score in the top row and left column.

False. You must convert it to a cumulative proportion.

Where do we locate the cumulative area in order to find a z-score?

In the inside of the table

After we locate the cumulative area inside the Standard Normal table, where do we locate the corresponding z-score?

In the left and top margins of the table

Where do we locate a z-score in the Standard Normal table?

In the left and top margins of the table

Where are the ones and tenths digits of a z-score given in a Standard Normal curve?

In the left hand column

Math SAT scores are Normally distributed with mean µ = 500 and standard deviation σ = 100. Using the 68-95-99.7 rule, what can you say about the area for the proportion of students who score greater than 550 on the SAT Math test? (No work necessary.)

The area is between 50% and 16%. Half of the curve or 50% is greater than the mean, µ = 500. 68% of the area is between 400 and 600. Half of 68% is 34% so 34% of the area is greater than 600. So the area greater than 550 has to be between 50% and 16%.

Math SAT scores are Normally distributed with mean µ = 500 and standard deviation σ = 100. Using the 68-95-99.7 rule, what can you say about the area for the proportion of students who score less than 650 on the SAT Math test? (No work necessary.)

The area is between 84% and 97.5%. 50% of the area is less than the mean, µ = 500. 84% of the area is less than one standard deviation above the mean, i.e., 84% is less than 600. And 2.5% is greater than 700 or, in other words, 97.5% is less than 700. So the area less than 650 must be between 84% and 97.5%.