BNAD 276 Exam 2

a population has a mean of 50 and a standard deviation of 10. a random sample of 256 is selected. the standard error of x bar is equal to

10/sr of 256

an investment strategy has an expected return of 12 percent and a standard deviation of 10 percent. If investment returns are normally distributed, the probability of earning a return of more than 32 percent is CLOSEST to:

2.5%

u

average

due to symmetry, the probability that the normal random variable Z is greater than 0 is equal to

equal to 0.5

the total area under the normal curve is __________.

equal to 1

if x is normally distributed with expected value u and standard deviation o, then x bar is normally distributed with

expected value u and standard deviation o/sr of n

which of the following statements is MOST accurate?

for the data that are normally distributed, 95% of the data will fall within 2 standard deviations

a characteristic of the normal distribution is that

it is symmetric around its mean

probability distribution of a discrete random variable is called probability ____________.

mass function

the normal distribution is completely described by these two parameters:

mean and variance

which of the following is an example of a continuous random variable

normal random variable

If X is normally distributed random variable, then

the mean, median, and mode are all equal

stratified sampling is preferred to cluster sampling when the objective is

to increase precision

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

P(-2<Z<-1)

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

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

stratified sampling

categorize observations with predetermined rationale (each is called a stratum), then select proportionate amount of observations from each group

if the shape of the population from which a simple random sample is drawn is normal, then the shape of the sampling distribution of x bar is

normal

the expected value of p bar is the

proportion of the population

simple random sampling

randomly select observations from an entire population--> each will have an equal chance of being selected (drawing from a hat, online generator)

a simple random sample is a sample of observations that is

representative of the population from which it was chosen

x bar

sample mean

x

sample number

n

sample size

o

standard deviation

a normal variable X is transformed into Z by

subtracting the mean, and then dividing by the standard deviation

True or false: if we had access to data that included the entire population, then the values of the parameters would be known and no statistical inference would be required.

true

True or false: the letter used to denote the standard normal random variable is Z

true

the expected value of X bar is equal to

u

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

uniform distribution

Consider data that are normally distributed. In order to transform a value z into it standardized value x, we use the following formula:

x=u+zo

inverse transformation (z to x)

x=u+zo

the probability that a continuous random variable X assumes a particular value x is

zero

If the population from which samples are drawn is not normally distributed, then the sampling distribution of the sample mean is:

always normally distributed

Central Limit Theorem

as sample size increases, the distribution of sample means of size n, randomly selected, approaches a normal distribution.

For a continuous random variable X, the number of possible values

cannot be counted

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

cumulative distribution function

uniform distribution

equal chance of all outcomes occuring, graph takes the shape of a rectangle (rolling dice)

for a continuous random variable, one characteristic of its probability density function f(x) is that

f(x)>0 for all values x of X

as a general guideline, the normal distribution approximation can be used to describe the sampling distribution of the sample mean when

n>30

random samples of size 400 are taken from a population whose population proportion is .25. the expected value of the sample proportion is

.25

the shape of the graph depicting the normal probability density function is_________.

bell shaped

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

between zero and one

cluster sampling

categorize observations (each is called a cluster), then randomly select a certain amount of clusters

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

continuous uniform distribution

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

continuous uniform distribution

which of the following can be represented by a discrete random variable?

the number of defective light bulbs in a sample of 5

all of the following are examples of random variables that likely follow a normal distribution EXCEPT

the number of states in the USA

the z table provides the cumulative probabilities for a given z. What does 'cumulative probabilities' mean?

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