6-1 SmartBook Assignment: Chapter 7 (Sections 7.1 through 7.4)

The Normal distribution is also called the ______ distribution.

Gaussian

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

The normal distribution is completely described by these two parameters.

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 less than or equal to any value x.

The mean of the standard normal distribution is ______?

ZERO

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

between zero and one, inclusive.

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.

blank 1: 1.3 blank 2: 0.07

The function used to find the area under the f(x) of a continuous random variable X up to any value x is called

the cumulative distribution function or CDF.

An example of a random variable that closely follows the normal distribution is _____.

weight of a box of cookies

Which of the following characteristics does NOT describe a Normal distribution?

It has finite upper and lower limits.

When using a standard normal table, P(-2 ≤ Z ≤ 2) is

.9544

A random variable is said to be continuous if it

1. can have decimal values. 2. is measured over an interval.

A random variable with the continuous uniform distribution has which of the following characteristics?

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.

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

FALSE Reason: Continuous RV's are defined on intervals.

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)

Match the Excel normal CDF to the explanation NORM.S.DIST <----> ________ NORM.DIST <----> _______

NORM.S.DIST matches Area to the left of a z score. NORM.DIST matches Area to the left of a given x value

Match the Excel inverse normal function to the explanation

NORM.S.INV matches Z score for a given cumulative area NORM.INV matches X value for a given cumulative area

Which Excel expression would be used to find the Z score associated with the lowest 2.5%?

NORM.S.INV(.025)

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

True

The normal distribution is asymptotic in the sense that _____.

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

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

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

An example of a random variable that closely follows the normal distribution is

weights of newborn babies.

The normal distribution is the most extensively used distribution in statistical studies because

1. Many physical measurements have a bell-shaped distribution. 2. Economic and financial data often display bell-shaped distributions. 3. It has important features used in sampling and estimation.

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

AREA

Which of the following is an example of a discrete random variable? 1. EXPONENTIAL 2. BINOMIAL 3. NORMAL 4. CONTINOUS UNIFORM

Binomial.

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).

Blank 1: -1.6 Blank 2: .05 Blank 3: .0495

To find the P(Z > 0.93) find the row containing _____ in the far left column. Then find the column containing _____ in the top row. P(Z > 0.93) = 1 - _____ (round to 4 decimals) = (round to 4 decimals).(Please use Appendix C-2.)

Blank 1: 0.9 Blank 2: .03 Blank 3: .8238 Blank 4: .1762

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

Blank 1: Z

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

Blank 1: mean or average Blank 2: standard Blank 3: deviation

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.

For normally distributed random variables, how would one verify the empirical rule percentages using z scores?

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

Which of the following is an example of a continuous random variable? 1. DISCRETE UNIFORM 2. NORMAL 3. POISSON 4. BINOMIAL

Normal

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

P(-1.96 ≤ Z ≤ 0)

Which probability statement below represents a cumulative probability?

P(Z ≤ -2.34)

Which of the following sample spaces would satisfy the definition of a continuous random variable?

X = [0,500]

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 random variable is said to be discrete if it has _____

countable number of values.

The normal distribution tails _____.

never touch the horizontal axis.

The standard deviation of the standard normal distribution is ______?

one