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) 20%

b) 40%

c) Mean = 62.5 seconds; Variance = 52.083 seconds

Step-by-step explanation:

The time it takes a hematology cell counter to complete a test on a blood sample is continuously distributed over the period of 50 to 75 seconds with probability f(x) = 0.04.

a) The percentage of tests require more than 70 seconds is:

$P(X>70) = 1- \frac{70-50}{75-50} \\P(X>70) =0.2 = 20\%$

b)The percentage of tests that require less than one minute (60 seconds) is:

$P(X<60) =\frac{60-50}{75-50} \\P(X>70) =0.4 = 40\%$

c) The mean and variance of a continuous distribution are determined by:

$M=\frac{A+B}{2}=\frac{50+75}{2}\\ M= 62.5\ seconds\\\\V=\frac{(B-A)^2}{12}=\frac{(75-50)^2}{12}\\ V= 52.083\ seconds$

Mean = 62.5 seconds.

Variance = 52.083 seconds.