Question

Suppose that the value of a stock varies each day from $10.82 to $25.17 with a uniform distribution. Find the third quartile, i.e., 75% of all days the stock is below what value

Answer 1

Answer: Third quartile =$21.58

Step-by-step explanation:

Let x be value of a stock .

For uniform distribution,

probability density function =  $\dfrac{1}{b-a}=\dfrac{1}{25.17-10.82}=\dfrac1{14.35}=\dfrac{100}{1435}$

Let a be the stock value such that P(x<a) =75% or 0.75

$\Rightarrow\ \int ^{a}_{10.82}f(x)\ dx=0.75\\\\\Rightarrow\ \int ^{a}_{10.82}\dfrac{100}{1435}\ dx=0.75\\\\\Rightarrow\dfrac{100}{1435}[x]^{a}_{10.82}=0.75\\\\\Rightarrow \dfrac{100}{1435}(a-10.82)=0.75\\\\\Rightarrow a-10.82=0.75\times\dfrac{1435}{100}\\\\\Rightarrow a-10.82=10.7625\\\\\Rightarrow a= 10.7625+10.82= 21.5825\approx 21.58$

Hence, 75% of all days the stock is below $21.58 or Third quartile =$21.58 .