stats chapter 6

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

(a+b)/2

probability that Z is greater than 1.32

.0934

find probability Z is greater than -2.22

.9868

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

0.50

find z value that satisfies P(Z>z) = 0.0951

1.31

z values that satisfies p(Z<_z) = 0.9207

1.41

area under a normal curve below its expected value is

0.5

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

0.5

an investment strategy has an expected return of 12% and a SD of 10%. If investment returns are normal, the probability of earning a return of less than 2%

16%

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)

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

P(Z<-1.5)

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

T/F. the expected value and the variance of the standard normal random variable Z are both zero

false

T/F; a discrete random variable can assume an uncountable number of values

false

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

mass function

the normal distribution is completely described by these two parameters

mean and variance

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

cannot be counted

the inverse transformation, x = u +zó is used to

compute x values for given probabilities

in order to transform a value x into its standardized value z, we use the following formula

z=(x-u)/ó

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

P(-2<Z<-1)

the graph depicting the normal probability density function is

bell shaped

which is an example of a continuous random variable?

normal random variable

which can be represented by a continuous random variable

the temp in Tampa, FL during july

an investment strategy has an expected return of 12% and a SD of 10%. If investment returns are normal, the probability of earning a return of more than 32% is closest to

2.5%

if X has a normal distribution with u=100 and ó=5, then the prob P(100<X<110) can be expressed in terms of the standard normal random variable Z as

P(0<Z<2)

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

between 0 and 1

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

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

zero

most accurate

normally distributed, 95% of data will fall within 2 SDs of the mean

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

suppose you were told that the delivery time of your new washing machine is equally likely over the time period 9am-12. If we define the random variable X as delivery time, then X follows the

continuous uniform distribution

total area under the normal curve is

equal to 1

for a continuous random variable X, how many distinct values can it assume over an interval

infinite

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

all our characteristics of the normal distribution except

it is a discrete distribution

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 probability distribution of a continuous random variable is called its

probability density function

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 square root (b-a)^2 / 12

standard deviation

a normal random variable X is transformed into Z by

subtracting the mean, and then dividing by the SD

all 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

manager of women's clothing store is projecting next months sales. Her low-end estimate of sales is $25,000 and her high-end estimate is $50,000. She decides to treat all outcomes of sales between these 2 values equally likely. If we define the random variable X as sales, then X follows the

uniform distribution