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The amount of time a service technician needs to change the oil in a car is uniformly distributed between 11 and 21 minutes. Let X = the time needed to change the oil on a car.

a. Write the random variable X in words. X = __________________.

b. Write the distribution.

c. Graph the distribution.

d. Find P (x > 19).

e. Find the 50th percentile.

Short Answer

Expert verified
  1. X=Amountoftimeneededtochangetheoil
  2. The distribution is uniform distribution.
  3. The graph of distribution is

d. P(x>19)=0.2

e. The50thpercentile is16.

Step by step solution

01

Part (a) Step 1: Given Information

Given in the question that, the amount of time a service technician needs to change the oil in a car is uniformly distributed between 11and 21minutes.

We need to write the random variable Xin words.

02

Part (a) Step 2: Solution 

According to the information from the question, the amount of time is uniformly distributed with parameter (11,21).

Therefore, the random variable Xcan be described as

X=Amountoftimeneededtochangetheoil

03

Part (b) Step 1: Given Information 

Given in the question that, the amount of time a service technician needs to change the oil in a car is uniformly distributed between 11and 21minutes.

We have to write the distribution.

04

Part (b) Step 2: Solution 

From the information given in the question, they clearly mentioned that the amount of time is uniformly distributed.

Therefore, the distribution is uniform distribution.

So,X~U(11,21)

05

Part (c) Step 1:  Given Information 

According to the information, the variable a=11and b=21.

We have to graph the distribution.

06

Part (c) Step 2: Solution 

Let's find the probability density function first,

The height of the data will be

f(x)=1ba

=12111

=110

The graph of the distribution given below,

07

Part (d) Step 1: Given Information 

From the information,

a=11

b=21

We have to findP(x>19)

08

Part (d) Step 2: Solution

The required probability can be computed as below,

P(x>19)=base×height

=(2119)×110

localid="1648011304762" =2×110

=0.2

09

Part (e) Step 1: Given Information 

From the information,

a=11

b=21

We have to find the50thpercentile.

10

Part (d) Step 2: Solution 

Let's calculate the 50thby using the given formula,

P(x<k)=base×height

0.50=(k11)×110

k-11=0.50×10

k=5+11

=16

Hence, The value of the 50thpercentile is 16

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