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.

0.1513

Step-by-step 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

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step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is