Question

The data that follow are the square footage (in 1,000 feet squared) of 28 homes.

The sample mean = 2.50 and the sample standard deviation = 0.8302. The distribution can be written as $X~U(1.5,4.5)$.

What is $P(x<3.5|x<4)$?

Short answer

The value of the$P(x<3.5\mid x<4)$is$0.80$.

Step-by-step solution

Given information

Table,

Sample mean = 2.50

Standard deviation = 0.8302

Solution

The probability density function to calculate $P(x<3.5\mid x<4)$for $1.5\le x\le 4.5$will be:

$f\left(x\right)=\frac{1}{4-1.5}$

$=\frac{1}{2.5}$

Thus, the value of $P(x<3.5\mid x<4)$is:

$P(x<3.5\mid x<4)=(3.5-1.5)\times \left(\frac{1}{2.5}\right)$

$=2\times \frac{1}{2.5}$

$=0.80$