Statistical Analysis 6-1: Chapter 7

A random variable is said to be continuous if it

- is measured over an interval - can have decimal values

The normal distribution is the most extensively used distribution in statistical studies because - it has important features used in sampling and estimation. - economic and financial data often display bell-shaped distributions. - it is the simplest of all the probability distributions. - many physical measurements have a bell-shaped distribution.

- it has important features used in sampling and estimation. - economic and financial data often display bell-shaped distributions. - many physical measurements have a bell-shaped distribution.

To find the P(Z ≤ -1.65) find the row containing ____ in the far left column. Then find the column containing ____ in the top row. The intersection of this row and column is ____ (Round to 4 decimals).

-1.6, .05, .0495

When using a standard normal table, P(-2 ≤ Z ≤ 2) is .6826 .9973 .4772 .9544

.9544

Choose the correct Excel function to find P(X > 110) for a normal random variable with μ = 100 and σ = 20. NORM.DIST(110,100,20,1) 1-NORM.DIST(110,100,20,1) 1-NORM.DIST(20,110,100,1) 1-NORM.S.DIST(110,100,20,1)

1-NORM.DIST(110,100,20,1)

To find P(0 ≤ Z ≤ 1.37) using Appendix C-1, find the row containing ____ in the far left column. Then find the column containing ____ in the top row. (Round the values to 2 decimal places.)

1.3 / 0.07

A random variable with the continuous uniform distribution has which of the following characteristics? - The probability distribution is bell shaped. - An equally likely chance of assuming any value within a specified range. - The probability distribution is based on n independent trials. - Assumes the values 0, 1, 2, -- - - n with different probabilities

An equally likely chance of assuming any value within a specified range.

Which of the following statements from the empirical rule is correct? Approximately 95% of values fall within 2 standard deviations of the mean for data with bell shaped histogram. Approximately 5% of values fall within 2 standard deviations of the mean for data with bell shaped histogram. Approximately 65% of values fall within 2 standard deviations of the mean for data with bell shaped histogram. Approximately 68% of values fall within 2 standard deviations of the mean for data with bell shaped histogram.

Approximately 95% of values fall within 2 standard deviations of the mean for data with bell shaped histogram.

The CDF for a continuous random variable gives the cumulative ____ under the PDF to the left of x.

Area

The probability that a discrete random variable equals any of its values is

Between zero and one, inclusive.

Which of the following is an example of a discrete random variable? - Binomial - Continuous Uniform - Exponential - Normal

Binomial

A random variable with an equally likely chance of assuming any value within a specified range is said to have which distribution?

Continuous Uniform Distribution

A random variable with an equally likely chance of assuming any value within a specified range is said to have which distribution? Binomial distribution. Continuous uniform distribution. Discrete uniform distribution. Geometric distribution.

Continuous uniform distribution

A random variable is said to be discrete if it has _____

Countable number of values

True or false: A continuous random variable can have a finite set of integer values.

False

For normally distributed random variables, how would one verify the empirical rule percentages using z scores? Find P(-2 ≤ Z ≤ 2) from a standard normal table and compare to 99.7%. Find P(-1 ≤ Z ≤ 1) from a standard normal table and compare to 95%. Find P(-2 ≤ Z ≤ 2) from a standard normal table and compare to 68%. Find P(-1 ≤ Z ≤ 1) from a standard normal table and compare to 68%.

Find P(-1 ≤ Z ≤ 1) from a standard normal table and compare to 68%.

The normal distribution is also called the ____ distribution.

Gaussian

Which Excel expression would be used to find the X value associated with the highest 10% if X has a mean = 100 and a standard deviation = 20? NORM.INV(.90,100,20) NORM.INV(.10,100,20) NORM.S.INV(.90,100,20)

NORM.INV(.90,100,20)

Which of the following is an example of a continuous random variable? - Binomial - Continuous Uniform - Exponential - Normal

Normal

Because the standard normal distribution is symmetrical about the mean 0, P(0 ≤ Z ≤ 1.96) is the same as P(0 ≤ X ≤ 1.96) P(-1.96 ≤ Z ≤ 1.96) P(0 ≤ Z ≤ -1.96) P(-1.96 ≤ Z ≤ 0)

P(-1.96 ≤ Z ≤ 0)

Which probability statement below represents a cumulative probability? P(Z = -2.34) P(0 ≤ Z ≤ 2.34) P(Z ≤ -2.34) P(Z > -2.34)

P(Z ≤ -2.34)

The normal distribution is completely described by these two parameters. - The population covariance and the population range. - The population mean and the population standard deviation. - The population mode and the population mean. - The population mode and the population size.

The population mean and the population standard deviation.

What is the use of the cumulative distribution function, F(x), of a continuous random variable? - To find the probability that X is not equal to any value x. - To find the probability that X is added to any value x. - To find the probability that X is less than or equal to any value x. - To find the probability that X is greater than or equal to any value x. - To find the probability that X is equal to any value x.

To find the probability that X is less than or equal to any value x.

True or false: The uniform model is used only when you have no reason to imagine that any X-values are more likely than others. True false question.

True

True or false: Under appropriate circumstances, many discrete random variables can be described by the normal distribution. True false question.

True

Which of the following sample spaces would satisfy the definition of a continuous random variable? 1.) X = {0,1,2,3} 2.) X = {odd integers between 5 and 15} 3.) X ={the number of days in the week that have the letter "r"} 4.) X = [0,500]

X = [0,500]

The letter used to denote the standard normal random variable is ____.

Z

The probability that a continuous random variable equals any of its values is

Zero

Consider a random variable X that denotes a random delivery time anywhere between 9 am and 10 am. X would reasonably be - a continuous uniform random variable. - a discrete random variable. - a positively skewed random variable. - a negatively skewed random variable.

a continuous uniform random variable

Any normal random variable X can be standardized by subtracting ____ the from x then dividing by the ____ ____ .

mean / standard / deviation

The normal distribution is asymptotic in the sense that _____________ - as the tails get closer and closer to the horizontal axis, they - eventually cross it. - as the tails get closer and closer to the horizontal axis, they eventually touch this axis. - the tails get closer and closer to the horizontal axis, but never touch it.

the tails get closer and closer to the horizontal axis, but never touch it.

The purpose of standardizing a normal random variable is - to change the scale to make all normal random variables fall between 0 and 100. - to create a common scale that then can be used for finding probabilities using tables or Excel. - to create a uniform distribution out of a normal distribution. - to convert a normal random variable into a positive random variable.

to create a common scale that then can be used for finding probabilities using tables or Excel.

An example of a random variable that closely follows the normal distribution is ______________. salary of NFL players scores on an easy statistics exam weight of a box of cookies names of high schools in a city

weight of a box of cookies

An example of a random variable that closely follows the normal distribution is - weights of newborn babies. - birth cities of newborn babies. - names of males in USA. - number of high schools in a city.

weights of newborn babies