Question

A store gathers some demographic information from their customers. The following chart summarizes the age-related information they collected:

Age	Number of Customers
<20<20	67
[20-29)	68
[30-39)	87
[40-49)	57
[50-59)	62
≥60≥60	58

One customer is chosen at random for a prize giveaway.

Enter your answers as either decimals or fractions, not as percents.

What is the probability that the customer is at least 20 but less than 60?    

(Round to 4 places)

What is the probability that the customer is either older than 60 or younger than 30?    

(Round to 4 places)

What is the probability that the customer is at least 60?    

(Round to 4 places)

Answer 1

Solution:

Given:

Age	Number of Customers
<20	67
[20-29)	68
[30-39)	87
[40-49)	57
[50-59)	62
≥60	58
	N = 399

Part a) What is the probability that the customer is at least 20 but less than 60?

P( 20 ≤ X < 60 ) =..............?

P( 20 ≤ X < 60 ) = Number of customers between 20 and 60 / N

Age	Number of Customers
<20	67
[20-29)	68
[30-39)	87
[40-49)	57
[50-59)	62
≥60	58
	N = 399

P( 20 ≤ X < 60 ) = ( 68+87+57+62) / 399

P( 20 ≤ X < 60 ) = 274 /399

P( 20 ≤ X < 60 ) = 0.6867

the probability that the customer is at least 20 but less than 60 is 0.6867

Part b) What is the probability that the customer is either older than 60 or younger than 30?  

P( X < 30 or X > 60) =...........?

P( X < 30 or X > 60) = P( X < 30) + P( X > 60)  

Age	Number of Customers
<20	67
[20-29)	68
[30-39)	87
[40-49)	57
[50-59)	62
≥60	58
	N = 399

where

P( X < 30) = Number of customers < 30 / N

P( X < 30) = (67+68) / 399

P( X < 30) = 135 / 399

and

P( X > 60) = Number of customers > 60 / N

P( X > 60) = 58 / 399

thus

P( X < 30 or X > 60) = P( X < 30) + P( X > 60)  

P( X < 30 or X > 60) = 135 / 399 + 58 / 399

P( X < 30 or X > 60) = ( 135 + 58 ) / 399

P( X < 30 or X > 60) = 193 / 399

P( X < 30 or X > 60) = 0.4837

the probability that the customer is either older than 60 or younger than 30 is 0.4837

Part c) What is the probability that the customer is at least 60?    

P( X  ≥ 60) =...........?

P( X  ≥ 60) = Number of customers ≥ 60 / N

Age	Number of Customers
<20	67
[20-29)	68
[30-39)	87
[40-49)	57
[50-59)	62
≥60	58
	N = 399

P( X  ≥ 60) = 58 / 399

P( X  ≥ 60) = 0.1454

the probability that the customer is at least 60 is 0.1454