Deck 17: Continuous Random Variables

Question 1

If X has density function f(x)= find k.

A) 12
B) 2
C)
D)
E) 24

Answer 1

24

Question 2

The random variable X has density function f(x)=
Find P(X > 2).Give answer in terms of e.

Answer 2

Question 3

The random variable X has density function f(x)=
Find (a)P
and (b)P
.

Answer 3

(a)
(b)

Question 4

The random variable X has density function f(x)=
Find μ and σ.

Question 5

The random variable X has density function f(x)=
Find the cumulative distribution function F over
.

Question 6

If X is uniformly distributed over
,what is the density function for X?

Question 7

The random variable X has density function f(x)=
Find P(X ≥ 4).Give answer in terms of e.

Question 8

Suppose the cumulative distribution function for the random variable X is given by
F(x)=
Find P(1 < X < 3).

Question 9

Suppose X is uniformly distributed over the interval
.Find (a)P(2 ≤ X ≤ 3)and (b)P(X ≥ 2).

Question 10

The random variable X has density function f(x)=
Find (a)P
and (b)P
.

Question 11

If the density function for the random variable X is f(x)=
,find k.

Question 12

The random variable X has density function f(x)=
Find μ and σ.

Question 13

The random variable X has density function f(x)=
Find the cumulative distribution function F over
.

Question 14

The random variable X has density function f(x)=
Find the cumulative distribution function F over
.

Question 15

If X is uniformly distributed over
,what is the density function for X?

Question 16

The random variable X has density function f(x)=
Find (a)P(20 ≤ X ≤ 40)and (b)P(X ≥ 40).

Question 17

Suppose the cumulative distribution function for the random variable X is given by
F(x)=
Find P(2 < X < 3).

Question 18

If the density function for the random variable X is f(x)=
,
find k.

Question 19

Suppose X is uniformly distributed over the interval
.Find P(2 < X < 4).

Question 20

If X has density function f(x)= find k.

A) 0
B) 1
C)
D) 6
E)

Question 21

If X is a normal random variable with μ = 30 and σ = 5,determine the Z-value that corresponds to X = 28.

Question 22

If X has density function f(x)= find σ.

A)
B)
C)
D)
E)

Question 23

The life expectancy (in years)of patients after they have contracted a certain disease is exponentially distributed with k = 0.4.Find the mean life expectancy and the standard deviation.

Question 24

If X has density function f(x)= find μ.

A)
B)
C)
D)
E) 2

Question 25

Suppose X has density function f(x)= Find P(2 < X < 3).

A)
B)
C)
D)
E)

Question 26

The life expectancy (in years)of a computer printer is distributed exponentially with k =
.If the printer's warranty lasts 3 years,what is the probability that a printer will break down during the warranty period?

Question 27

The length of time (in minutes)that a person arriving at a bus stop must wait for a bus is uniformly distributed with density function f(x)=
where 0 ≤ x ≤ 15.Find the mean waiting time and the standard deviation.

Question 28

If Z has a standard normal distribution,find P(0 < Z < 1.48).

Question 29

Suppose X is uniformly distributed over the interval .Find P(3 < X < 8).

A)
B)
C)
D)
E)

Question 30

The life expectancy (in years)of a computer printer is distributed exponentially with k =
.If the printer's warranty lasts 3 years,what is the probability that a printer will last more than 10 years?

Question 31

Suppose the time (in minutes)passengers must wait for an airplane is uniformly distributed with density function f(x)=
where 0 ≤ x ≤ 60 and f(x)= 0 elsewhere.What is the probability that a commuter must wait more than 0 minutes?

Question 32

Suppose the time (in minutes)applicants must wait to receive a driver's examination is uniformly distributed with density function f(x)=
where 0 ≤ x ≤ 40 and f(x)= 0 elsewhere.What is the probability that an applicant must wait less than 25 minutes?

Question 33

If X is a normal random variable with μ = 16 and σ = 2,determine the Z-value that corresponds to X = 23.

Question 34

Suppose the time (in minutes)applicants must wait to receive a driver's examination is uniformly distributed with density function f(x)=
where 0 ≤ x ≤ 40 and f(x)= 0 elsewhere.What is the probability that an applicant must wait more than 35 minutes?

Question 35

Suppose X has density function f(x)= Find P(X < 1).

A) 2 - 2
B) - 1
C)
D) 1 - 2
E) 1 -

Question 36

Suppose X is uniformly distributed over the interval .Find P(X > 5).

A) 03.
B) 0.4
C) 0.5
D) 0.6
E) 0.7

Question 37

If X has density function f(x)= find c such that P(X < c)=
)

A)
B) 2
C) 2
D) 8
E) 4

Question 38

The length of time (in minutes)that a person arriving at a train station must wait for a train is uniformly distributed with density function f(x)=
where 0 ≤ x ≤ 20.Find the mean waiting time and the standard deviation.

Question 39

If X has density function f(x)= find μ.

A)
B)
C)
D)
E)

Question 40

The life expectancy (in years)of a keyboard is distributed exponentially with k =
.If the keyboard's warranty lasts 2 years,what is the probability that a keyboard will break down after the warranty expires?

Question 41

If Z has a standard normal distribution,find P(Z > 0.12).

Question 42

If X is normally distributed with μ = 8 and σ = 2,find P(3 ≤ X ≤ 8).

Question 43

If X is normally distributed with μ = 18 and σ = 2,find P(11 ≤ X ≤ 16).

Question 44

If Z has a standard normal distribution,find P(2.5 ≤ Z ≤ 3).

Question 45

If Z has a standard normal distribution,find P(-3 ≤ Z ≤ -0.5).

Question 46

If Z has a standard normal distribution,find P(|Z| <
).

Question 47

If Z has a standard normal distribution,find P(-0.65 < Z < 1.92).

Question 48

If Z has a standard normal distribution,find P(|Z| > 1.75).

Question 49

If X is normally distributed with μ = 10 and σ = 2,find P(4 ≤ X ≤ 12).

Question 50

If X is normally distributed with μ = 100 and σ = 10,find P(X < 115).

Question 51

If Z has a standard normal distribution,find P(-2 ≤ Z ≤ -1).

Question 52

If Z has a standard normal distribution,find P(Z > -1.81).

Question 53

If Z has a standard normal distribution,find P(2.2 < Z < 3.5).

Question 54

If X is normally distributed with μ = 12 and σ = 2,find P(12 ≤ X ≤ 15).

Question 55

If X is normally distributed with μ = 25 and σ = 5,find P(20 ≤ X ≤ 35).

Question 56

If X is normally distributed with μ = 20 and σ = 4,find P(16 ≤ X ≤ 18).

Question 57

If Z has a standard normal distribution,find P(Z > 2σ).

Question 58

If X is normally distributed with μ = 100 and σ = 10,find P(X < 118).

Question 59

If Z has a standard normal distribution,find P(-1 ≤ Z ≤ 2).

Question 60

If Z has a standard normal distribution,find P(Z < -1.23).

Question 61

Suppose X is normally distributed with mean 100 and standard deviation 20.Without using tables,determine the approximate value of P(80 < X < 100).

A) 0.997
B) 0.95
C) 0.68
D) 0.50
E) 0.34

Question 62

If X is normally distributed with μ = 150 and σ = 30,find P(90 < X < 180).

A) 0.1359
B) 0.8185
C) 0.3185
D) 0.8243
E) 0.8173

Question 63

The life (in hours)of light bulbs of a certain brand is normally distributed with mean 1200 and standard deviation 100.What percentage of such bulbs will burn more than 1250 hours?

A) 13.62
B) 20.47
C) 30.85
D) 41.73
E) 48.26

Question 64

If Z is a standard normal variable,find
such that P(-
< Z <
)= 0.823.

Question 65

If Z has a standard normal distribution,state the mean and standard deviation of Z.

Question 66

If X is normally distributed with μ = 80 and σ = 8,find P(X < 74).

A) 0.2734
B) 0.7734
C) 0.2266
D) 0.7732
E) 0.7266

Question 67

The scores on an examination are normally distributed with μ = 75 and σ = 10.What percentage of the scores are between 70 and 90?

Question 68

If X is normally distributed with μ = 60 and σ = 5,find P(X > 72).

A) 0.0082
B) 0.0123
C) 0.2731
D) 0.2968
E) 0.4918

Question 69

If Z has a standard normal random variable and P(Z >
)= 0.9938,

Question 70

If Z has a standard normal random variable and P(Z >
)= 0.4539,

Question 71

If X is normally distributed with μ = 20 and σ = 5,find such that P(X >
)= 0.025.

A) 18.6
B) 21.96
C) 27.2
D) 29.8
E) 31.6

Question 72

If Z is a standard normal variable,find
such that P( Z ≥
)= 0.9918.

Question 73

If X is normally distributed with μ = 40 and σ = 6,find P(X ≥ 37).

Question 74

If X is normally distributed with mean μ and standard deviation σ,then what is the approximate probability that μ - 2σ ≤ X ≤ μ + 2σ?

A) 0.5
B) 0.68
C) 0.95
D) 0.997
E) 0.999

Question 75

The life (in hours)of light bulbs of a certain brand is normally distributed with mean 1000 and standard deviation 100.What percentage of such bulbs will burn more than 950 hours?

A) 40.95
B) 72.15
C) 68.34
D) 65.54
E) 69.15

Question 76

If X is normally distributed with μ = 50 and σ = 10,find such that P(X <
)= 0.9938.

A) 25
B) 50
C) 75
D) 80
E) 100

Question 77

If X is normally distributed with μ = 50 and σ = 8,find P(X ≤ 44).

Question 78

Suppose X is normally distributed with mean 80 and standard deviation 15.Without using tables,determine the approximate value of P(65 < X < 95).

A) 0.997
B) 0.95
C) 0.68
D) 0.50
E) 0.33

Question 79

Suppose X is normally distributed with μ = 80 and σ = 15.Without using tables,approximate P(50 < X < 80).

Question 80

The scores on an examination are normally distributed with μ = 500 and σ = 100.What percentage of the scores are less than 360?