BUS 245 exam 3

The probability that a normal random variable X is less than its mean is equal to

0.50

The accompanying table shows a portion of the z table. Find the z value that satisfies P(Z ≤ z) = 0.0222. z 0.00 0.01 0.02 -2.2 0.0139 0.0136 0.0132 -2.1 0.0179 0.0174 0.0170 -2.0 0.0228 0.0222 0.0217

-2.01

The inverse transformation, x= μ+ zσ is used to

compute x values for given probabilities

Parameter is a

constant

the sample size required to approximate the normal distribution depends on

how much the population varies from normality

If X has a normal distribution with μ= 100 and σ= 5, then the probability P(90 < X < 95) can be expressed in terms of the standard normal random variable X as

P(-2 < z < -1)

What does it mean to say that the exponential distribution is "memoryless"?

it has a constant failure rate

Which of the following continuous distributions are positively skewed and bounded below by zero?

lognormal distribution and exponential distribution

a confidence interval narrows if the following is accomplished

the sample size increases and the chose confidence level decreases

Bias can occur in sampling. Bias refers to

the tendency of a sample statistic to systematically over or under estimate a population parameter

A manager of a women's clothing store is projecting next month's sales. Her low-end estimate of sales is $25,000 and her high-end estimate is $50,000. She decides to treat all outcomes for sales between there two values as equally likely. If we define the random variable X as sales, the X follows the

uniform distribution

Consider the data that are normally distributed. In order to transform a standard normal value z into its unstandardized value x, we use the following formula:

x= μ+ zσ

Which of the following random variable is depicted with a bell-shaped curve?

a normal random variable

Estimate is

a particular value of an estimator

Due to symmetry, the probability that the standard normal random variable Z is greater than 0 is

equal to 0.5

The total area under the normal curve is

equal to 1

The probability distribution of a discrete random variable is called its probability

mass function

In order to construct a confidence interval for u, the sampling distribution of the estimator x* must follow or approximately follow a(n) _____ distribution

normal

random samples of 400 are taken from a population whose pop proportion is 0.25. The expected value of the sample proportion is

0.25

A random sample of 60 observations results in 42 successes. What is the point estimate of the population proportion of successes?

0.7

a population has a mean of 100 and a standard deviation of 12. A random sample of 36 is selected. The SD of x is equal to

2

What is the value of zα/2 for a 99% confidence interval for the population mean?

2.576

A 95% confidence interval for the population mean is calculated as (40, 80). The margin of error for this interval is ____

20

It is known that the length of a certain product X is normally distributed with μ= 20 inches. How is the P(X < 20) related to the P(X < 16)?

P(X < 20) is greater than P(X < 16)

If Y= e^x has a lognormal distribution, what can be said of the distribution of the random variable X?

X follows a normal distribution

In a statistical problem, a population consists of

all items of interest

if the population from which the sample is drawn is normally distributed, then the sampling distribution of the sample mean is

always normally distributed

The probability that a discrete random variable X assumes a particular value x is

between 0 and 1

the central limit theorem states that, for any distribution, as n gets larger, the sampling distribution of the sample mean becomes

closer to a normal distribution

Suppose you were told the the delivery time of your new washing machine is equally likely over the time period 9 am to noon. If we define the random variable X as delivery time, then X follows the

continuous uniform distribution

For a continuous random variable, one characteristic of its probability density function f(x) is that the area under f(x) over all possible values of x is

equal to 1

when a sample statistic is used to make inferences about a population parameter, it is referred to as an

estimator

All of the following are examples of random variables that likely follow a normal distribution except

income in the USA

What is a primary requirement of a "good" sample?

it is a representative of the population we are trying to describe

A characteristic of the normal distribution is that

it is asymptotic

A characteristic of a normal distribution is that

it is symmetric around its mean

The further a population proportion deviates from p= 0.50, the _________ the sample size required in order to satisfy a normal approximation.

larger

the parameter p represents the

population proportion

A normal random variable X is transformed into Z by

subtracting the mean, and then dividing by the standard deviation

Which of the following can be represented by a continuous random variable?

the high daily temperature in Tampa, Florida during the month of July, measured in degrees

The exponential distribution is related to which distribution?

the poisson distribution

For a discrete random variable X,

there are a countable number of possible values

Selection bias occurs when

there is a systematic exclusion of certain groups from consideration for the sample

nonresponce bias occurs when

those responding to a survey or poll differ systematically from the non-respondents

stratified sampling is preferred to cluster sampling when the objective is to

to increase precision

if we had access to data that included the entire population, then the values of the parameters would be known an no statistical inference would be required

true

the expected value of x- is equal to

upside down h

the probability distribution of the sample mean is commonly referred to as the

x-

__________ involves diving a population into mutually exclusive and exhaustive groups, called clusters, and then selecting a random sample from these clusters for analysis.

cluster sampling

For a continuous random variable X, the cumulative distribution function F(x) provides the probability that X is

less than or equal to any value x

The z table provides the cumulative probability for a given value z, What doe "cumulative probability" mean?

the probability that Z is less than or equal to a given z value

The exponential random variable is bounded below by

0

The mean and variance of the standard normal distribution are ___________, respectively.

0 and 1

If an exponential distribution has the rate parameterλ = 5, then the expected value is

1/5

How many parameters are needed to fully describe any normal distribution?

2

Since the z table provides the cumulative probabilities for a given value of z, how can we calculate P(Z>z)?

=1-P(Z ≤ z)

A sample is

a subset of the population

a continuous random variable has the uniform distribution on the interval [a,b] if its probability density function f(x)

is constant for all x between a and b, and 0 otherwise

the expected value of p- is the

proportion of successes in the population

Statistic is a

random variable