. A normal population has a mean of 80.0 and a standard deviation of 14.0. a. Compute the probability of a value between 75.0 and 90.0. b. Compute the probability of a value of 75.0 or less. c. Compute the probability of a value between 55.0 and 70.0. 19. Suppose the Internal Revenue Service reported that the mean

a. 0.40198

b. 0.36049

c. 0.20046

Step-by-step explanation:

To solve for this we make use of the z score formula.

z-score formula is

z = (x-μ)/σ,

where

x is the raw score

μ is the population mean

σ is the population standard deviation.

a. Compute the probability of a value between 75.0 and 90.0.

For x = 75

From the question, we know that

mean of 80.0 and a standard deviation of 14.0.

z = (x - μ)/σ

z = 75 - 80/ 14

z = -0.35714

Using the z score table to find the probability

P-value from Z-Table:

P(x = 75) = P(z = -0.35714)

= 0.36049

For x = 90

z = 90 - 80/14

z = 0.71429

Using the z score table to find the probability

P-value from Z-Table:

P(x = 90) = P(z = 0.71429)

= 0.76247

The probability of a value between 75.0 and 90.0 is:

75 < x < 90

= P( x = 90) - P(x = 75)

= 0.76247 - 0.36049

= 0.40198

Therefore, probability of a value between 75.0 and 90.0 is 0.40198

b. Compute the probability of a value of 75.0 or less.

For x = 75

From the question, we know that

mean of 80.0 and a standard deviation of 14.0.

z = (x - μ)/σ

z = 75 - 80/ 14

z = -0.35714

Using the z score table to find the probability

P-value from Z-Table:

P(x ≤ 75) = 0.36049

c. Compute the probability of a value between 55.0 and 70.0.

For x = 55

From the question, we know that

mean of 80.0 and a standard deviation of 14.0.

z = (x - μ)/σ

z = 55 - 80/ 14

z = -1.78571

Using the z score table to find the probability

P-value from Z-Table:

P(x = 55) = P(z = -1.78571)

= 0.037073

For x = 70

z = 70 - 80/14

z = -0.71429

Using the z score table to find the probability

P-value from Z-Table:

P(x = 70) = P(z = -0.71429)

= 0.23753

The probability of a value between 55.0 and 70.0 is:

55 < x < 70

= P( x = 70) - P(x = 55)

= 0.23753 - 0.037073

= 0.200457

Approximately to 4 decimal place = 0.20046

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation:

x² + 11x + 18 < 0  

[-11 ± sqrt(121 - 72)]/2 = (-11 ± 7)/2  

solution: (-9, -2)

step-by-step explanation: