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