Business Statistics Chapter 7 Smartbook

For an exponential random variable X with λ = 2.3 arrivals/minute, P(X > 1 minute) =

.1003

Suppose the MTBE is 3.4 seconds. Then P(X ≤ 5 seconds) =

.7702

To find the z score associated with the highest 1% of a normal distribution, recognize that the area to the left of this z score is

.99

The mean and standard deviation of the exponential distribution are

1/λ and 1/λ

The median of an exponential distribution with λ = 0.3 arrivals per minute is

2.3 minutes

If given the mean time between arrivals is 10 minutes then the average arrival rate is

6/hour

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 is an example of a discrete random variable?

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

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

To find the z score associated with the lowest 2.5% of a normal distribution, search for _______ in the middle of the cumulative standard normal table.

Blank 1: .025 or .0250

For a continuous random variable X with a = 10 and b = 20, P(X ≤ 14) =

Blank 1: .4, 0.4, 2/5, or 4/10

A normal random variable X has a mean = 100 and a standard deviation = 20. P(X ≤ 110) = _____

Blank 1: .6915, 0.6915, or .69146

A normal random variable X has a mean = 100 and a standard deviation = 20. P(X ≤ 110) = _________ . Round your answer to 4 decimals

Blank 1: .6915, 0.6915, or .69146

A normal random variable X has a mean = 100 and a standard deviation = 20. For X = 110, the standardized value is _______

Blank 1: 0.5, .5, or 1/2

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.)

Blank 1: 1.3 or 1.30 Blank 2: .07 or 0.07

The CDF for a continuous random variable gives the cumulative

Blank 1: area

For a continuous distribution, the standard deviation is the _____ ________ of the variance

Blank 1: square Blank 2: root

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.

If X is exponential with an average = 3.4 seconds, to find P(X ≤ 5 seconds) using Excel the correct expression would be

EXPON.DIST(5,1/3.4,1)

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

False

Match the Excel normal CDF to the explanation

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

Choose the correct Excel function to find P(Z ≤0.87)

NORM.S.DIST(.87,1)

Which of the following is an example of a continuous random variable?

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)

The PDF of the continuous uniform distribution has which shape?

Rectangular

The probability that a continuous random variable takes on a particular value is zero because of which of the following reasons?

The area under a curve AT a certain point is zero.

The normal distribution is completely described by these two parameters.

The population mean and the population standard deviation.

Which of the following statements about the variance of a continuous random variable are true?

The variance is the weighted average of the squared deviations from the mean. The standard deviation is the square root of the variance.

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

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

True

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

X = [0,500]

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 triangular distribution that has a mode = 0 and has a lower limit = -2.45 and an upper limit = 2.45 is similar to

a standard normal

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

between zero and one, inclusive.

A random variable is said to be continuous if it

can have decimal values. is measured over an interval.

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

countable number of values.

One characteristic of a well-defined probability density function of a continuous random variable X is that the area under the curve, f(x,) over all values of x is

equal to one.

One condition of a well-defined probability density function of a continuous random variable X is that f(x) is

greater than zero for all values of X.

additional flashcard set

https://quizlet.com/607236381/6-1-smartbook-assignment-chapter-7-sections-71-through-74-flash-cards/

It is meaningful to compute the probability that a continuous random variable

is between two numbers. is greater than or equal to a number. is less than or equal to a number.

The triangular distribution

is bounded by the interval [a, c]. is useful for what-if analysis.

The triangular distribution

is useful for what-if analysis. is bounded by the interval [a, c].

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. many physical measurements have a bell-shaped distribution.

It is appropriate to approximate the Poisson distribution with the normal distribution when

lan is large

Any normal random variable X can be standardized by subtracting the ____________ from x then dividing by the ___________ ___________

mean standard deviation

Binomial probabilities can be difficult to calculate, and therefore appropriate to approximate, when

n is large.

The normal distribution tails ____________

never touch the horizontal axis.

The standard deviation of the standard normal distribution is ______?

one

If the continuous uniform random variable, X, assumes the values a and b as its lower and upper limits respectively, then (b−a)212/ √(b-a)212 represents the _____ of X.

standard deviation

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.

When a random process counts the number of arrivals over a random time interval we are also interested in the ________between two arrivals.

time

The purpose of standardizing a normal random variable is

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 ______________.

weight of a box of cookies

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

weights of newborn babies.

The mean of the standard normal distribution is ______?

zero

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

zero.

To approximate the Poisson distribution with the normal distribution let

μ = λ σ = λ (square root)