Simplify the complex fraction. In complete sentences, explain the process that you followed to simplify the fraction. Include the LCD and simplified form in your answer. Complete your work in the space provided or upload a file that can display math symbols if your work requires it. a-9/a

1-3/a

the answer of the question is given above pls check it



A. 0.9015

B. 0.1658

C. 0.0132

Step-by-step explanation:

Given

Mean, μ of commuting time in New York is 39.7 minutes

Standard Deviation, σ = 7.5 minutes

Let x represent the commute time

For Normal Distribution, z = (x - μ) /σ

A. x is less than 30 minutes

P(x<30) = P(x - μ < 30 - μ)

P(x<30) = P((x - μ)/ σ < (30 - μ)/ σ)

P(x<30) = P(z < (30 - μ)/ σ)

P(x<30) = P(z < (30 - 39.7) / 7.5)

P(x<30) = P(z < (-9.7/7.5)

P(x<30) = P(z < -1.29)

P(x<30) = P(z > 1.29)

P(x<30) = 0.9015 From z table

B. x is between 30 and 35

P(30>x<35) = P(30 -μ > x - μ < 35 - μ)

P(30>x<35) = P((30 -μ)/σ < (x - μ)/σ < (35 - μ) / σ)

P(30>x<35) = P((30 -μ)/σ < z < (35 - μ) / σ)

P(30>x<35) = P((30 -39.7)/7.5 < z < (35 - 39.7) / 7.5)

P(30>x<35) = P(-9.7/7.5 < z < -4.7/7.5)

P(30>x<35) = P(-1.29 < z < -0.63)

There are two points on the same side here; we calculate both probabilities and subtract to give

P(30>x<35) = P(-1.29 < z < 0) - P(0 < z < -0.63)

P(30>x<35) = P(0 < z < 1.29) - P(0 < z < 0.63)

P(30 > x < 35) = 0.9015 - 0.7357

P(30 > x < 35) = 0.1658

C. x is between 30 and 50

P(30>x<50) = P(30 -μ > x - μ < 50 - μ)

P(30>x<50) = P((30 -μ)/σ < (x - μ)/σ < (50 - μ) / σ)

P(30>x<50) = P((30 -μ)/σ < z < (50 - μ) / σ)

P(30>x<50) = P((30 -39.7)/7.5 < z < (50 - 39.7) / 7.5)

P(30>x<50) = P(-9.7/7.5 < z < 10.3/7.5)

P(30>x<50) = P(-1.29 < z < 1.37)

There are two points on different sides here; calculate both probabilities and add to give

P(30>x<50) = P(-1.29 < z < 0) + P(0 < z < 1.37)

P(30>x<50) = -P(0 < z < 1.29) + P(0 < z < 1.37)

P(30 > x < 50) = -0.9015 + 0.9147

P(30 > x < 50) = 0.0132