A population of sightless, cave-dwelling crayfish was recently discovered in Mex

Question

A population of sightless, cave-dwelling crayfish was recently discovered in Mexico.The tail-lengths of all 434 crayfish in the population living in this underground pool were measured and it was determined that the mean tail length was 8.2 cm and the standard deviation of tail length was 0.98.

What proportion of the population has tail lengths as short as or shorter than 5.9cm?Show all work neatly.

What proportion of the population has tail lengths as long as or longer than 8.0cm?Show all work neatly.

Explanation / Answer

MEAN = 8.2

STANDARD DEVIATION = 0.98

Z SCORE = (X-MEAN)/STANDARD DEVIATION

A) P(X<5.9) =

For x = 5.9, the z-value z = (5.9-8.2 ) / 0.98 = -2.34

Hence P(x < 5.9) = P(z < -2.34) = [area to the left of -2.34] = 0.0096

B) P(X>8) =

For x = 8, z = (8 - 8.2) / 0.98 = -0.20

Hence P(x > 8) = P(z > -0.2) = [total area] - [area to the left of -0.2]

= 1 - 0.4207 = 0.5793

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