Calculator Norm

Practice with the calculator and Normal distributions

Multiple Choice

Blood pressure According to a health information website, the distribution of adults’ diastolic blood pressure (in millimeters of mercury) can be modeled by a Normal distribution with mean 70 and standard deviation 20. What percent of adults have a diastolic blood pressure between 50 and 70?

• 68%

• 34%

• 16%

• 95%

Multiple Choice

Blood pressure According to a health information website, the distribution of adults’ diastolic blood pressure (in millimeters of mercury) can be modeled by a Normal distribution with mean 70 and standard deviation 20. What percent of adults have a diastolic blood pressure between 30 and 110?

• 34%

• 68%

• 16%

• 95%

Using the calculator

• Determine what the lower and upper bounds are for the area under the Normal curve for which you are looking

• Press 2nd, then VARS (DISTR) to get to the Distribution menu. Choose 2: normalcdf

• normalcdf(lower: , upper: , mean: , SD: )

Open Ended

Blood pressure According to a health information website, the distribution of adults’ diastolic blood pressure (in millimeters of mercury) can be modeled by a Normal distribution with mean 70 and standard deviation 20. A diastolic pressure above 100 for an adult is classified as very high blood pressure. About what proportion of adults have very high blood pressure according to this criterion? (Write out the calculations and calculator commands needed for this problem. Then restate the answer in the form of a sentence. If this were an FRQ, you would also need to draw the Normal curve and shade the area being described.)

Open Ended

Blood pressure According to a health information website, the distribution of adults’ diastolic blood pressure (in millimeters of mercury) can be modeled by a Normal distribution with mean 70 and standard deviation 20.

According to the same health information website, a diastolic blood pressure between 80 and 90 indicates borderline high blood pressure. About what percent of adults have borderline high blood pressure?

(Write out the calculations and calculator commands needed for this problem. Then restate the answer in the form of a sentence.)

The invNorm command

Let's say you know that your blood pressure is at the 53rd percentile. Let's figure out what diastolic blood pressure you have.

On the calculator press 2nd, VARS (DISTR). Then select 3: invNorm

invNorm (area: 0.53, mean: 70, SD: 20) = 71.505

We describe 53% as 0.53 of the area under the Normal curve. You must convert the percentile or percent of the area into a decimal or else you'll get an error in the calculator.

A person with a diastolic blood pressure at the 53rd percentile will have a diastolic blood pressure of 71.505.

Multiple Choice

Blood pressure According to a health information website, the distribution of adults’ diastolic blood pressure (in millimeters of mercury) can be modeled by a Normal distribution with mean 70 and standard deviation 20.

Mr. Aldana's doctor told him that his diastolic blood pressure is at the 37th percentile. What is Mr. Aldana's diastolic blood pressure?

• 59.5

• -3

• 63

• -0.332

Open Ended

Blood pressure According to a health information website, the distribution of adults’ diastolic blood pressure (in millimeters of mercury) can be modeled by a Normal distribution with mean 70 and standard deviation 20.

Find the 85th percentile of diastolic blood pressures.

(Write out the calculations and calculator commands needed for this problem. Then restate the answer in the form of a sentence.)

Open Ended

IQ test scores

Scores on the Wechsler Adult Intelligence Scale (an IQ test) for the 20- to 34-year-old age group are approximately Normally distributed with μ= 110 and σ = 25.

What percent of people aged 20 to 34 have IQs between 125 and 150?

Open Ended

IQ test scores

Scores on the Wechsler Adult Intelligence Scale (an IQ test) for the 20- to 34-year-old age group are approximately Normally distributed with μ= 110 and σ = 25.

MENSA is an elite organization that admits as members people who score in the top 2% on IQ tests. What score on the Wechsler Adult Intelligence Scale would an individual aged 20 to 34 have to earn to qualify for MENSA membership?

Normal Probability Plots

Normal Probability Plot

This Normal probability plot shows what a Normal distribution looks like.

The dots have the coordinates (data value, z-score if it is a Normal distribution). Notice the y-axis in this graph shows the percentile of the data. Since the y-coordinate is the z-score if the distribution were Normal, then it makes a diagonal line when the distribution really is Normal.

Right skewed

This shows the Normal probability plot and the associated histogram for data with a right skew.

Notice how the Normal probability plot is curved at the lower end and trails off with very few points at the right end. These are two signs that the distribution is skewed.

Left skew

This image shows a left-skewed distribution's Normal probability plot and the associated histogram of the distribution.

Notice how the Normal probability plot has very few points on the lower end and how the points curve up on the higher end of the plot.

Carbon dioxide emissions

The following figure is a Normal probability plot of the emissions of carbon dioxide (CO₂) per person in 48 countries. Use the graph to determine if this distribution of CO₂ emissions is approximately Normal.

Carbon dioxide emissions

The sharp curve in the Normal probability plot suggests that the data are right-skewed. This can be seen in the steep, nearly vertical section in the lower left. These numbers were much closer to the mean than would be expected in a Normal distribution, meaning the values that would be in the left tail are piled up close to the center of the distribution.

Refrigerators

Consumer Reports magazine collected data n the usuable capacity (in cubic feet) of a sample of 36 side-by-side refridgerators. Here are the data:

12.9, 13.7, 14.1, 14.2, 14.5, 14.5, 14.6, 14.7, 15.1, 15.2, 15.3, 15.3, 15.3, 15.3, 15.5, 15.6, 15.8, 16.0, 16.0, 16.2, 16.2, 16.3, 16.4, 16.5, 16.6, 16.6, 16.6, 16.8, 17.0, 17.0, 17.2, 17.4, 17.4, 17.9, 18.4

Enter this data into List 1 in your calculator.

Press STAT. Then select 1: Edit... This will take you to your lists.

If you need to delete old data from a list, press STAT, then select 4: ClrList and then enter L1 (press 2nd and "1" to type L1).

Open Ended

Refrigerators

Using the data from the previous slide, and with mean 15.825 cubic feet and standard deviation 1.217, is this distribution of refrigerator capacities approximately Normal?

Justify your answer based on the 68-95-99.7 Rule.

Open Ended

Refrigerators

In your calculator, create a Normal Probability Plot.

You've already entered your data into List 1.

Now press 2nd and Y= (STAT PLOT) to access the Stat Plot screen.

Press ENTER to select Plot1.

Highlight ON and press ENTER

For Type: select the last type of graph, which looks like a diagonal line of dots.

Make sure that Data List says L1.

Now press ZOOM and select 9: Zoomstat.

This will show you the Normal Probability Plot for the refrigerators data. Does this graph show an approximately Normal distribution? Describe how you know.

Open Ended

The Normal probability plot displays data on the areas (in thousands of square miles) of each of 50 states. Use the graph to determine if the distribution of land area is approximately Normal.