Question

select the correct answer.
the table gives the probability distribution of the number of books sold in a day at a bookstore. what is the probability of 16 or more books being sold on a given day?

number of books sold in a day	0 - 5	6 - 10	11 - 15	16 - 20	21 - 25

a. 0.220
b. 0.201
c. 0.464
d. 0.019

Explanation:

Step1: Recall total probability rule

The sum of all probabilities in a probability distribution is \(1\). Let \(P(21 - 25)=x\). So, \(0.110 + 0.206+0.464 + 0.201+x = 1\).

Step2: Calculate sum of known probabilities

First, sum the known probabilities: \(0.110+0.206 = 0.316\); \(0.316 + 0.464=0.78\); \(0.78+0.201 = 0.981\).

Step3: Find probability for 21 - 25

Since total probability is \(1\), \(x=1 - 0.981=0.019\)? Wait, no, wait. Wait, the question is probability of 16 or more. 16 or more includes 16 - 20 and 21 - 25. So we need to find \(P(16 - 20)+P(21 - 25)\). Wait, first, let's correct. Wait, total probability: \(0.110 + 0.206+0.464 + 0.201+P(21 - 25)=1\). So \(P(21 - 25)=1-(0.110 + 0.206+0.464 + 0.201)=1 - 0.981 = 0.019\)? Wait, no, that can't be. Wait, no, wait, maybe I misread. Wait, the options: A is 0.220, B is 0.201, C is 0.464, D is 0.019. Wait, no, wait, 16 or more: 16 - 20 (0.201) and 21 - 25. Wait, but if total probability is 1, then 0.110 + 0.206 + 0.464 + 0.201 + P(21 - 25) = 1. So P(21 - 25) = 1 - (0.110 + 0.206 + 0.464 + 0.201) = 1 - 0.981 = 0.019. Then 16 or more is 0.201 + 0.019 = 0.220. Ah! There we go. So step by step:

Step1: Calculate total of known probabilities (excluding 21 - 25)

Sum \(0.110 + 0.206 + 0.464 + 0.201 = 0.981\).

Step2: Find probability for 21 - 25

\(P(21 - 25)=1 - 0.981 = 0.019\).

Step3: Find probability of 16 or more (16 - 20 and 21 - 25)

\(P(16\text{ or more})=P(16 - 20)+P(21 - 25)=0.201 + (1 - 0.981)=0.201 + 0.019 = 0.220\).

Wait, let's re - do:

1. First, recall that in a probability distribution, the sum of all probabilities is 1. So we first find the probability for the 21 - 25 category.

1. Sum of probabilities for 0 - 5, 6 - 10, 11 - 15, 16 - 20: \(0.110+0.206 + 0.464+0.201=0.981\).

1. Then, probability for 21 - 25: \(1 - 0.981 = 0.019\).

1. Now, "16 or more" includes 16 - 20 and 21 - 25. So we add their probabilities: \(0.201+0.019 = 0.220\).

Answer:

A. 0.220