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Chapter 5: Question 83 (page 354)

Suppose that the value of a stock varies each day from \(16to\)25with 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" \)19and\(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.

Short Answer

Expert verified

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

b. The probability that the value of the stock is between $19and$22is 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 $21is0.5714.

Step by step solution

01

Defining the height of Probability distribution

It is given thatX~U(16,25)

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

f(x)=1b-a=125-16=19

02

Finding the probability that the value of the stock is more than $19.

a) The required probability can be calculated as below:

P(x>19)=base脳height=(25-19)脳19=69=0.67
03

Finding the probability that the value of the stock is between $19 and $22.

b) The required probability can be calculated as below:

P(19<x<22)=base脳height=(22-19)脳19=39=0.33

04

Finding the upper quartile - 25% of all days the stock is above what value

c) The upper quartile can be calculated as below :

P(x>k)=base脳height鈬�0.25=(25-k)脳19鈬�9脳0.25=25-k鈬�k=22.75

05

Finding the probability that the stock is more than $21,given that the stock is greater than $18,

d) The required probability can be calculated as below:

P(x>21x>18)=base脳height=(25-21)脳1(25-18)=4脳17=0.5714

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