exam 2

The area under a normal curve below its expected value is

0.50

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

1/5

A population has a mean of 100 and a standard deviation of 10. A random sample of 25 is selected. The expected value of x bar is equal to

100

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 less than 2 percent is CLOSEST to

16%

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

16%

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

2

If X has a normal distribution with u=100 and sigma=5, then 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 P(X<20) related to the P(X<16)?

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

Due to symmetry, the probability that the normal random variable Z is greater than 1.5 is equal to

P(Z<-1.5)

A continuous random variable X follows the uniform distribution with lower limit of a and an upper limit of b. The expected value of X is calculate as

a + b / 2

A variation in production caused by a specific event or factor that can usually be identified and eliminated is called

assignable variation

The inverse transformation, x=u+zsigma is used to

compute x values for given probabilities.

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

equal to 0.52

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

equal to one

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

equal to one

The total area under the normal curve is

equal to one

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

f(x) is greater than or equal to 0 for all values x of X

For a continuous random variable X it is only meaningful to calculate the probability that the value of the random variable

falls within some specified interval

true/false: a discrete random variable can assume an uncountable number of values

false

true/false: a parameter is a numerical measure that describes a sample

false

true/false: the expected value and the variance of the standard normal random variable Z are both zero

false

A random variable X follows the continuous uniform distribution if

it has an equally likely chance of assuming any value within a specified range

In general, the variability between sample mean is _____ the variability between observations

less than

The value of the finite population correction factor is always

less than one

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

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

n is greater than or equal to 30

The exponential random variable is

nonnegative

The exponential distribution is

not symmetric

The variance of the standard normal distribution is equal to

one

The exponential distribution is based entirely on

one parameter

We use the finite population correction factor to

reduce the sampling variation of x bar and p bar (for added precision gained by sampling a larger percentage of the population)

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

sampling distribution of x bar

The variance of x bar, which is equal to sigma^2/n is

smaller than the variance of the individual observations of sigma^2

Assignable variation is caused by

specific events that can usually be identified and eliminated

What can be said about the expected value and standard deviation of an exponential distribution?

the expected value is equal to the standard deviation

If we were to sample repeatedly from a given population, the average value of the sample means will equal

the population mean

The standard deviation of x bar is calculated as

the positive square root of the variance of x bar

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

the temperature in Tampa, Florida during the month of july

Selection bias occurs when

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

true/false: the letter used to denote the standard normal random variable is Z

true

Consider 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=u+zsigma

The exponential random variable is bounded below by

zero

A sporting goods manufacturer wants to ensure that the balls it produces have a diameter of 30 inches. The standard deviation of 0.5inches. The manufacturer samples 25 balls every 5 hours and calculates the mean diameter. The lower control limit is how many inches?

29.7

In general, the control limits of a control chart are set at what standard deviation from the centerline?

3

A sporting goods manufacturer wants to ensure that the balls it produces have a diameter of 30 inches. The standard deviation of 0.5inches. The manufacturer samples 25 balls every 5 hours and calculates the mean diameter. The upper control limit is how many inches?

30.3

If an exponential distribution has an expected value equal to 5, then the standard deviation equals

5

If an exponential distribution has standard deviation equal to 0.20, then the rate parameter is

5

The general rule for using the finite correction factor is that the sample constitutes at least what percent of the population?

5%

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

=1-P(Z, less than or equal to, z)

The probability that the normal random variable Z is less than 1.5 is equal to

P(Z>-1.5)

true/false: a production process is in control if the sample means on a control hart start below the centerline, trend upward, and do not cross the upper control limit

false