Chapter 6 - The Normal Probability Distribution

Question 1

Variables can assume values in an uncountable set (e.g., an interval in real line).

Answer 1

Continuous Random Variables

Question 2

A __ __ describes the probability distribution of a continuous random variable.

Answer 2

smooth curve

Question 3

The depth or density of the probability, which varies with x, may be described by a mathematical formula f (x ), called the __ __ or__ __ __ for the random variable x.

Answer 3

probability distribution or probability density function

Question 4

The area under the curve is equal to __.

Answer 4

1

Question 5

P(a ≤ x ≤ b) =

Answer 5

area under the curve between a and b.

Question 6

There is no probability attached to any single value of x. That is, P(x = a) = ?

Answer 6

0

Question 7

Thus, P(x ≤ a) =

Answer 7

P(x < a)

Question 8

One important continuous random variable is the __ __ __

Answer 8

normal random variable

Question 9

Uniform Distribution The probability density function of a uniform random variable is flat:

Answer 9

.

Question 10

Variables can assume values in an uncountable set (e.g., an interval in real line).

Answer 10

Continuous Random Variables

Question 11

A __ __ describes the probability distribution of a continuous random variable.

Answer 11

smooth curve

Question 12

The depth or density of the probability, which varies with x, may be described by a mathematical formula f (x ), called the __ __ or__ __ __ for the random variable x.

Answer 12

probability distribution or probability density function

Question 13

The area under the curve is equal to __.

Answer 13

1

Question 14

P(a ≤ x ≤ b) =

Answer 14

area under the curve between a and b.

Question 15

There is no probability attached to any single value of x. That is, P(x = a) = ?

Answer 15

0

Question 16

Thus, P(x ≤ a) =

Answer 16

P(x < a)

Question 17

One important continuous random variable is the __ __ __

Answer 17

normal random variable

Question 18

Uniform Distribution The probability density function of a uniform random variable is flat:

Answer 18

.

Question 19

Exponential Distribution

The probability density function of an exponential random variable is:

where __ is the mean.

Answer 19

where µ is the mean.

Question 20

__ __ variable is often used to model the lifetime of electric components

Answer 20

Exponential random

Question 21

Survival probability:

Answer 21

Question 22

Memoryless Property:

Answer 22

Question 23

The Normal Distribution

The formula that generates the normal probability distribution is:

Answer 23

Question 24

To find P(a < x < b), we need to find..

Answer 24

the area under the appropriate normal curve.

Question 25

To simpify the tabulation of these areas, we __ each value of x by expressing it as a __

Answer 25

Standardize

z-score

Question 26

the number of standard deviations (s) it lies from the mean (m)

Answer 26

z-score

Question 27

The Standard Normal (z) Distribution

Mean = ?; Standard deviation = ?
When x = m, z = ?
Symmetric about z = ?
Values of z to the left of center are __

Values of z to the right of center are__

Total are under the curve is __.

Answer 27

Mean = 0; Standard deviation = 1
When x = m, z = 0
Symmetric about z = 0
Values of z to the left of center are negative
Values of z to the right of center are positive
Total area under the curve is 1.

Question 28

The four digit probability in a particular row and column of Table 3 gives the__ __ __ __ to the __ that particular value of z.

Answer 28

area under the z curve

left

Question 29

To find an area to the left of a z-value,.
To find an area to the right of a z-value,
To find the area between two values of z,

Answer 29

find the area directly from the table

find the area in Table 3 and subtract from 1.

find the two areas in Table 3, and subtract one from the other.

Question 30

To find an area for a normal random variable x with mean µ and standard deviation σ, __ or __ the interval in terms of __.

Answer 30

standardize or rescale

z

Question 31

When n is large, and p is not too close to zero or one, areas under the normal curve with

mean np and variance npq

can be used to __ __ __.

Answer 31

approximate binomial probabilities

Question 32

Make sure to include the entire rectangle for the values of x in the interval of interest. This is called the __ __.

Answer 32

Continuity Correction.

Question 33

Approximating the Binomial

Continuity Correction

Standardize the values of x using:

Answer 33

Question 34

We must make sure of what before approximating the binomial with normal approximation?

Answer 34

np > 5

nq > 5