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Chapter 5: Q. 11 (page 346)

f(x),a continuous probability function, is equal to 112and the function is restricted to 0鈮�x鈮�12. What is P(0<x<12)?

Short Answer

Expert verified

TheP(0<x<12)is1

Step by step solution

01

Given Information 

Given in the question that, the f(x)remains a continuous probability function. It is equal to 112and the function is restricted to 0鈮�x鈮�12.

We have to find what is P(6鈮�x鈮�8).

02

Concept Introduction 

Consider the data in the question; the continuous probability function is written as follows:

f(x)=112,鈥呪赌呪赌呪赌�0鈮�x鈮�120,鈥呪赌呪赌呪赌�otherwise

Here, Xfollows a uniform distribution.

Therefore, the area between (0<x<12)creates a rectangle with xaxis.

Then the base is base=(12鈭�0)and height is height=112

03

Calculation

For continuous random variable X, P(c<x<d)=P(c鈮�x鈮�d).

The value of P(0<x<12)is:

P(0<x<12)=base脳height

=(12鈭�0)脳112

=1212

=1

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Most popular questions from this chapter

Use the following information to answer the next eight exercises. A distribution is given as X~U(0,12).

Draw the graph of the distribution for P(x>9).

Find the probability that x falls in the shaded area.

At an urgent care facility, patients arrive at an average rate of one patient every seven minutes. Assume that the duration between arrivals is exponentially distributed.

a. Find the probability that the time between two successive visits to the urgent care facility is less than 2minutes.

b. Find the probability that the time between two successive visits to the urgent care facility is more than 15minutes.

c. If 10minutes have passed since the last arrival, what is the probability that the next person will arrive within the next five minutes?

d. Find the probability that more than eight patients arrive during a half-hour period.

f(x)for a continuous probability function is15 , and the function is restricted to 0鈮�x鈮�5. What is P(x<0)?

The time (in minutes) until the next bus departs a major bus depot follows a distribution with f(x)=120 where X goes from 25 to 45 minutes.

a. Define the random variable. X=

b. X~

c. Graph the probability distribution.

d. The distribution is (name of distribution). It is (discrete or continuous).

e. 渭=

f. 蟽=

g. Find the probability that the time is at most 30 minutes. Sketch and label a graph of the distribution. Shade the area of interest. Write the answer in a probability statement.

h. Find the probability that the time is between 30 and 40 minutes. Sketch and label a graph of the distribution. Shade the area of interest. Write the answer in a probability statement.

i. P(25<x<55)= . State this in a probability statement, similarly to parts g and h, draw the picture, and find the probability.

j. Find the 90th percentile. This means that 90% of the time, the time is less than

k. Find the 75th percentile. In a complete sentence, state what this means. (See part j.)

1. Find the probability that the time is more than 40 minutes given (or knowing that) it is at least 30 minutes.
See all solutions

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