Question

Red drum, sciaenops ocellatus, is a game fish found in the Atlantic Ocean and in the Gulf of Mexico. A reasonable estimate of the mean length of a red drum caught, tagged, and released is 15.4 inches with standard deviation 4.5 inches. Current regulations by Texas Parks and Wildlife only allow red drums between 20 and 28 inches to be kept. Fish outside this range must be thrown back. Assuming the distribution of lengths is approximately normally distributed, what is the probability that a red fish caught on the Texas coast can be brought home for dinner? Sketch the normal curve, label the mean and SD, and shade the area of interest. Write your answer using correct probability notation, finding all appropriate z-scores.

Answer 1

0.1513

Explanation:

mean= 15.4

SD=4.5

P(20<X<28)

P((20-15.4)/4.5 < Z < (28-15.4)/4.5)

P(1.022 < Z< 2.8 )

From Z distribution table,

P(Z<2.8)= 0.99744

P(Z<1.022)= 0.84614

P(1.022 < Z< 2.8 )= P(Z<2.8)- P(Z<1.022)

= 0.99744-0.84614

= 0.1513