Question

The probability density function of the time it takes a hematology cell counter to complete a test on a blood sample is f(x)=0.04 for 50
A) What percentage of tests require more than 70 seconds to complete?
b) What percentage of tests require less than one minute to complete?
c) Determine the mean and variance of the time to complete a test on a sample.

Answer 1

Answer:

a) 0.2

b) 0.4

c) Mean  = 62.5

Variance = 52.083              

Step-by-step explanation:

We are given the following information in the question:

$f(x) = 0.4$

a = 50, b = 75

We are given a uniform distribution.

a) P(x > 70)

$P(x > 70)\\=1 - P( \leq 70)\\\\=1-\displaystyle\int^{70}_{50}0.04 ~dx\\\\=1-0.04(70-50)\\=0.2$

b) P(x < 60)

$P(x < 60)\\\\=\displaystyle\int^{60}_{50}0.04 ~dx\\\\=0.04(60-50)\\=0.4$

c) Mean:

$\mu = \displaystyle\frac{a+b}{2}\\\\\mu = \frac{50+75}{2} = 62.5$

Variance:

$\sigma^2 = \displaystyle\frac{(b-a)^2}{12}\\\\= \displaystyle\frac{(75-50)^2}{12} = 52.083$