Question

Use the table to find the probabilities that a​ person's total charges during the period are the following.

This table shows the probabilities of a person accumulating specific amounts of credit card charges over a​12-month period.

Charges		Probability
Under​ $100		0.34
	​$100−​$499	0.18
	​$500−​$999	0.15
	​$1000−​$1999	0.12
	​$2000−​$2999	0.05
	​$3000−​$4999	0.06
	​$5000−​$9999	0.09
​$10,000 or more		0.01

What is the probability that a​ person's total charges are between ​$3000 and ​$4999​?----------------

​(Type an integer or decimal rounded to two decimal places as​ needed.)

What is the probability that a​ person's total charges are less than ​$1000​?--------------------

​(Type an integer or decimal rounded to two decimal places as​ needed.)

What is the probability that a​ person's total charges are over ​$4999​?------------------

​(Type an integer or decimal rounded to two decimal places as​ needed.)

Answer 1

Solution :

Given table is

Charges Probability

Under​ $100 0.34

​ $100 − ​$499 0.18

​$500 − ​$999 0.15

​ $1000 − ​$1999 0.12

​ $2000 − ​$2999 0.05

​ $3000 − ​$4999 0.06

​ $5000 − ​$9999 0.09

​ $10,000 or more 0.01

=> The probability that a​ person's total charges are between ​$3000 and ​$4999 is 0.06

P(3000 <= x <= 4999) = 0.06 (from given table)

=> The probability that a​ person's total charges are less than ​$1000 is 0.67   

P(x < 1000) = P( Under​ $100 ) + P($100 − ​$499) + P(​$500 − ​$999)

= 0.34 + 0.18 + 0.15

= 0.67

=> The probability that a​ person's total charges are over ​$4999 is 0.10

P(x > 4999) = P($5000 − ​$9999) + P(​$10,000 or more)

= 0.09 + 0.01

= 0.10