Question 1

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

Accepted Answer

(a)  ; 
(b)

Question 2

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?

Accepted Answer

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

Question 3

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?

Accepted Answer

1

Question 4

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

Accepted Answer

The answer of If Z has a standard normal distribution,find...

Question 5

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

Accepted Answer

The answer of The random variable X has density function...

Question 6

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

Accepted Answer

The answer of If Z has a standard normal distribution,find...

Question 7

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

Accepted Answer

The answer of The random variable X has density function...

Question 8

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

Accepted Answer

The answer of If Z has a standard normal distribution,find...

Question 9

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

Accepted Answer

The answer of The random variable X has density function...

Question 10

If X is normally distributed with μ = 90 and σ = 10,find P(65 < X < 80).

Accepted Answer

A)   0.1048
B)   0.1232
C)   0.1347
D)   0.1428
E)   0.1525

Question 11

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

Accepted Answer

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

Question 12

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

Accepted Answer

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

Question 13

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

Accepted Answer

A)   
B)   
C)   
D)   
E)   2

Question 14

Playing a fair "shell game," the probability of winning the game should be given by p =  
.One person plays the game 50 times but only wins 7 times.Using n = 50,approximate P(X = 7)by using the normal approximation.

Accepted Answer

The answer of Playing a fair "shell game," the probability...

Question 15

A professor claims that there is only a 15% chance of earning an "A" in her class.At the end of the semester,40 of the 278 students earn "A's." Using n = 278 and p = 0.15,approximate P(X = 40)by using the normal approximation.

Accepted Answer

The answer of A professor claims that there is only...

Question 16

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

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 17

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

Accepted Answer

The answer of The random variable X has density function...

Question 18

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

Accepted Answer

The answer of If X is uniformly distributed over ...

Question 19

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

Accepted Answer

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

Question 20

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

Accepted Answer

The answer of If the density function for the random...

Exam 17: Continuous Random Variables

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

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?

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?

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

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

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

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

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

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

If X is normally distributed with μ = 90 and σ = 10,find P(65 < X < 80) .

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

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

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

Playing a fair "shell game," the probability of winning the game should be given by p = .One person plays the game 50 times but only wins 7 times.Using n = 50,approximate P(X = 7)by using the normal approximation.

A professor claims that there is only a 15% chance of earning an "A" in her class.At the end of the semester,40 of the 278 students earn "A's." Using n = 278 and p = 0.15,approximate P(X = 40)by using the normal approximation.

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

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

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

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

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