STATS CH 6
All of the following are characteristics of the normal distribution EXCEPT
It is a discrete distribution.
True or false: Statistical inference is generally based on the assumption of the normal distribution.
True
The normal distribution is completely described by these two parameters:
mean and variance
A continuous random variable X follows the uniform distribution with a lower limit of a and an upper limit of b. The ______ of X is calculated using the formula √(b−a)2/12(b-a)2/12.
standard deviation
For a continuous random variable, P(a≤X≤b) equals
the area under f(x) from a to b.
Since the z table provides the cumulative probabilities for a given value of z, what is the P(Z < z)?
the value found by looking up z in the table.
Percntiles for a normally distributed random variable can be found most easily by using which of the following formulas?
x = μ + zσ
Consider data that are normally distributed. In order to transform a value x into it standardized value z, we use the following formula
z = x−μσ
The z table in the text provides the cumulative probability for a given value z. What does "cumulative probability" mean?
P(Z≤z)
Which of the following is true about the formula for finding the 83rd percentile? Select all that apply.
The percentile would be greater than the mean. The z-value would be positive.
The probability that a continuous random variable X assumes a particular value x is
zero.
The height of the probability density function f(x) of the uniform distribution defined on the interval [a,b] is
1b−a1b-a between a and b, and zero otherwise.
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 continuous random variable X follows the uniform distribution with a lower limit of a and an upper limit of b. The expected value of X is calculated as
a+b2
The shape of the graph depicting the normal probability density function is
bell shaped
For a z-value greater than 0, the P(Z<z) will be
between 0.5 and 1.
The inverse transformation, x = μ + zσ is used to
compute x values for given probabilities
Which of the following BEST describes the shape of the normal distribution?
unimodal and symmetric
Why is the normal distribution such an important probability distribution
The normal distribution plays a key role in statistical inference.
Due to symmetry, the probability that the standard normal random variable Z is greater than 0 is
equal to 0.5
The P(z1<Z<z2), where z1 and z2 are both positive and z1<z2, must be
less than 0.5.
For all normally distributed random variables, the
the mean, the median, and the mode are all equal.
P(Z<0) equals ____. Select all that apply
P(Z≤0) P(Z>0) 0.5
Which of the following are true about the normal curve? Select all that apply.
The area above the mean equals the area below the mean. The total area under the curve equals 1.
The mean and variance of the standard normal distribution are ______, respectively
0 and 1
The probability that a normal random variable X is less than its mean is equal to
0.50
Due to symmetry, the probability that the normal random variable Z is greater than 1.5 is equal to
P(Z < -1.5)
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
Why is the normal distribution such an important probability distribution?
The normal distribution plays a key role in statistical inference.
Which one of the following is true?
The standard normal distribution is a special case of the normal distribution.
The purpose of the standard transformation is to
allow for the calculation of probabilities of any normal random variable.
Transforming normal random variables
allows for the z-table to be used for determining probabilities.
A continuous random variable X can assume
an infinite number of values over some interval.
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
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
For a continuous random variable X it is only meaningful to calculate the probability that the value of the random variable Multiple choice question.
falls within some specified interval.
A random variable X follows the continuous uniform distribution if Multiple choice question.
it has an equally likely chance of assuming any value within a specified range.
TA random variable X follows the continuous uniform distribution if
it has an equally likely chance of assuming any value within a specified range.
For a z-value less than 0, the P(Z<z) will be
less than 0.5.
A normal random variable X is transformed into Z by
subtracting the mean, and then dividing by the standard deviation.
Since the z table provides the cumulative probabilities for a given value of z, what is the P(0 < Z < z)?
the result of subtracting 0.5 from the value found by looking up z in the table.
If the P(Z<z) is greater than 0.5, then
z must be positive.
