veheca
19.03.2021 •
Mathematics
A petri dish is a small, shallow dish of thin glass or plastic, used especially for cultures in bacteriology. A 2-inch-radius petri dish, containing nutrients upon which bacteria can multiply, is smeared with a uniform suspension of bacteria. Subsequently, spots indicating colonies of bacteria appear. The distance of the center of the first spot to appear from the center of the petri dish is a variable with density curve y= x/2 for 0 < x <2 and y=0 otherwise.
a. Graph the density curve of this variable.
b. Show that the area under this density curve to the left of any number x between 0 and 2 equals x2/4.
c. What percentage of the time is the distance of the center of the first spot to appear from the center of the petri dish
1. at most 1 inch?
2. between 0.25 inch and 1.5 inches?
3. more than 0.75 inch?
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Ответ:
a) attached below
b) Area = 1/2 ( base ) (height )
= 1/2 ( x ) ( x/2)
= x^2 / 4
C) i)25% ii) 54.69% iii) 85.94%
Step-by-step explanation:
Given density curve y = x/2 for 0 < x < 2 and y = 0
a) Graph the density curve of this variable
attached below
b) show that the area under the density curve to the left of any number x between 0 and 2 equals x^2/4
base of triangle = x
height = x/2
Hence to show the area under the density curve is equal to x^2/4 we will calculate the area to the left
Area = 1/2 ( base ) (height )
= 1/2 ( x ) ( x/2)
= x^2 / 4
c) Determine the percentage of the time of the distance of the center of the first spot to appear from the center of the petri dish
i) At most 1 inch
(area to the left of 1 ) = 1^2 / 4
= 1/4 = 0.25 ≈ 25%
ii) between 0.25 inch and 1.5 inches?
( area between 0.25 and 1.5 ) = ( area to the left of 1.5 ) - ( Area to the left of 0.25 )
= (1.5^2 / 4 )- ( 0.25^2 / 4 )
= 0.5469 = 54.69%
iii) more than 0.75 inch
( Area to the right of 0.75 ) = 1 - (0.75^ / 4)
= 0.8594 = 85.94 %
Ответ:
can you give me the answers
Step-by-step explanation: