Ch 3

Use the schematic curve and the z-table to find the proportion of a population less than z = -1.96 and greater than z = +1.96

0.9500

What is the appropriate mathematics to use to find a right body area

1 - An area from the z-table.

What is the appropriate mathematics to use to find a middle body area

1 - a left area from the z-table - a right area from the z-table.

use the schematic curve and the z-table to find the z-score that bounds the top 2.02% of a population

2.05

Intelligent Quotient (IQ) scores are standardized for population to have a mean score of 100 and a standard deviation score of 15. With this knowledge, what percent of the population are eligible to join the Mensa organization (need IQ > 130)?

2.28%

At a local secondary school, the school children were known to run a race with the race times distributed normally with a mean time of 450 seconds and a standard deviation time of 50 seconds. With this information, what is the shortest time and the longest time of the middle 95% of the children

352 seconds, and 548 seconds

Use the schematic curve and the z-table to find what are the z-scores for the first quartile (Q₁), and for the third quartile (Q₃)

(Q₁) is at z = -0.67, and (Q₃) is at z = +0.67 .

In a recent past year, the scores of students taking the ACT college entrance test were found to be distributed normally with a mean score of 18.6 and a standard deviation score of 5.85. What is the probability that a randomly chosen student from this population would have an ACT score lower than 21

0.6591

What is the range of z-scores

-∞ < 𝓏 < +∞

Use the schematic curve and the z-table to find the probability of an individual having a z-score greater than +2.00

0.0228

For a city where the prices of new homes were distributed normally with a mean price of $150,000 and a standard deviation price of $11,000, what proportion of new homes are mid priced (between $125,000 and $139,000)

0.1471

in a recent past year, the scores of students taking the ACT college entrance test were found to be distributed normally with a mean score of 18.6 and a standard deviation score of 5.17. What is the probability that a randomly chosen student from this population would have an ACT score higher than 21.6

0.2810

Use the schematic curve and the z-table to find the probability of an individual in a population following the standard normal curve being less than (or greater than) the mean

0.500

For a city where the prices of new homes were distributed normally with a mean price of $150,000 and a standard deviation price of $1,700, what percentage of home buyers paid more than $152,074

11.12%

The times to complete a mile long race for boys in a local secondary school was known to be normally distributed with a mean time of 460 seconds and a standard deviation time of 60 seconds. With this population, what time separates the fastest 10% of the boys from the other 90%. Note that a faster boy completes the race in less seconds

383.3

At a local secondary school, the school children were known to run a race with the race times distributed normally with a mean time of 450 seconds and a standard deviation time of 50 seconds. With this information, what is the shortest time and the longest time of the middle third (34%) of the children

428 seconds, and 472 seconds

In a factory packaging corn chips, the weight of corn chips put into each bag by a dispensing machine was distributed normally with a mean weight of 48.5 ounces and a standard deviation weight of 0.2 ounces. What weight of corn chips separates the lightest 67% of the bags from the other 33%

48.59 ounces

The times to complete a mile long race for boys in a local secondary school was known to be normally distributed with a mean time of 460 seconds and a standard deviation time of 60 seconds. With this population, what time separates the fastest 90% of the boys from the other 10%. Note that a faster boy completes the race in less seconds

536.8

In a city where the prices of new homes were found to be distributed normally with a mean price of $150,000 and a standard deviation price of $900, what percentage of these new homes cost less than $148,623

6.30%

The tread life of a brand of tire is distributed normally with a mean of 60,000 miles and a standard deviation of 1,000 miles. What mileage separates the longest lasting 4% of these tires (have the highest mileage) from the other 96%

61750

For a city where the prices of new homes were distributed normally with a mean price of $150,000 and a standard deviation price of $1,1,00, what percentage of new homes are mid priced (between $146,500 and $151,500)?

91.24%

What is the appropriate mathematics to use to find a two-tail area

An area from the z-table + an area from the z-table.

What is the appropriate mathematics to use to find a left tail area

An area from the z-table.

Which of the following answers is NOT true of a statistical event.

An event is an area under a normal curve

Why is the distribution of a data set so important

Because the distribution can be used to find the probability of an event

What are the critical parameters of a normal curve

Mean (µ) and standard deviation (σ)

what is the mean (µ) and standard deviation (σ) of the standard normal distribution (z-distribution)

Mean = 0, and standard deviation = 1.

Why is the probability of an event so important in the science of statistics?

Probability of an event can be used to make a better decision.

In the standard normal distribution, what are z-scores used to describe?

The event on the x-axis.

Which of the following answers is NOT true about why the Empirical Rule focuses out to (µ±3σ), but not beyond

The information beyond µ±3σ is much harder to calculate

What is the appropriate mathematics to use to find a right-side area

The larger area from the z-table - the smaller area from the z-table.

What information does an area under the normal curve give?

The probability of an event.

The z-curve is a graph of what distribution

The standard normal distribution.

For a side area in the schematic curve, how many lines are drawn and on which side of the curve are they drawn?

Two lines on the same side.

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area under the curve

On a real number line, a change in the mean shifts a normal curve horizontally, and a change in the standard deviation shifts the normal curve vertically

false

Only one critical parameter is needed to calculate probability with a normal curve.

false

The probability of an event can mean two things: 1. The proportion of the population described by the event. 2. The chance an individual will be randomly selected.

false

There are an infinite number of standard normal distributions

false

x-Values have no units of measurement associated with them.

false

How many normal curves are possible?

infinitely many

A normal curve can be described with one specific mathematical equation, if the values of the variables are known.

true

All normal curves look the same WHEN they are plotted on a graph in terms of their mean +/- their standard deviations.

true

For the Shapiro-Wilk test for normality, a P-value = 0.25 means that the data follow a normal shape

true

Standard deviation (σ) is another way to give the width of a normal curve.

true

The Schematic Curve for z-scores, with a second x-axis in terms of the mean and standard deviation of the x-values, gives the Schematic Curve for x-values.

true

The areas defined in the Empirical Rule of statistics are valid for all normal curves

true

The standard normal distribution ( z-distribution) follows the Empirical Rule of statistics.

true

the area under the standard normal curve = 1.

true

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x-value

are the two equations below the same equation with one equation just a reorganization of the other equation? z=x−μ/σ x=μ+z∗σ

yes

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z-score