Chapter 5: Question 83 (page 354)

Suppose that the value of a stock varies each day from $$16 to $ 25$ with a uniform distribution.
a. Find the probability that the value of the stock is more than $$19$ .
b. Find the probability that the value of the stock is between role="math" localid="1648188993020" $$ 19 and $22$ .
c. Find the upper quartile - $25 %$ of all days the stock is above what value? Draw the graph.
d. Given that the stock is greater than $$ 18$ , find the probability that the stock is more than $$ 21$ .

Expert verified

a. The probability that the value of the stock is more than $$ 19$ is $0.67$

b. The probability that the value of the stock is between $$ 19 and $ 22$ is $0.33$ .

c. The upper quartile $- 25 %$ of all days the stock is above $22.75$ .

d. The probability that the stock is more than $$ 21 is 0.5714$ .

Step by step solution

It is given that $X ~ U (16, 25)$

Therefore, the height or probability distribution of the data will be:

$f (x) = \frac{1}{b - a} = \frac{1}{25 - 16} = \frac{1}{9}$

a) The required probability can be calculated as below:

P (x > 19) = b a s e \times h e i g h t = (25 - 19) \times \frac{1}{9} = \frac{6}{9} = 0.67

b) The required probability can be calculated as below:

$P (19 < x < 22) = b a s e \times h e i g h t = (22 - 19) \times \frac{1}{9} = \frac{3}{9} = 0.33$

c) The upper quartile can be calculated as below :

$P (x > k) = b a s e \times h e i g h t \Rightarrow 0.25 = (25 - k) \times \frac{1}{9} \Rightarrow 9 \times 0.25 = 25 - k \Rightarrow k = 22.75$

d) The required probability can be calculated as below:

P (x > 21 x > 18) = b a s e \times h e i g h t = (25 - 21) \times \frac{1}{(25 - 18)} = 4 \times \frac{1}{7} = 0.5714

Unlock Step-by-Step Solutions & Ace Your Exams!

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.