Problem 7-35 A satellite range prediction error has the standard normal distribution with mean 0 NM and standard deviation 1 NM. Find the following probabilities for the prediction error: (a) less than 1.17 NM Probability (b) between 1.04 NM and 1.99 NM Probability (c) greater than 0.93 NM Probability (d) between 0.24 NM and 0.73 NM Probability (e) less than or equal to 2.3 NM Probability (f) greater than 2.22 NM or less than .65 NM Probability (g) greater than or equal to 2.0 NM Probability\

Kindly check explanation

Step-by-step explanation:

For a normal distribution with :

Mean(m) = 0

Standard deviation (s) = 1

Calculate :

(a) less than 1.17 NM Probability

Zscore = (x - m) / s = (1.17 - 0) / 1 = 1.17

P(z < 1.17) = 0.879

(b) between 1.04 NM and 1.99 NM Probability

Zscore = (x - m) / s = (1.04 - 0) / 1 = 1.04

P(z < 1.04) = 0.8508

Zscore = (x - m) / s = (1.99 - 0) / 1 = 1.99

P(z < 1.99) = 0.9767

(0.9767 - 0.8508) = 0.1259

(c) greater than 0.93 NM Probability

P(Z > 0.93) = 1 - p(Z < 0.93) = 1 - 0.8238 = 0.1762

(d) between 0.24 NM and 0.73 NM Probability

P(Z < 0.24) = 0.5948

P(Z <0.73) = 0.7673

0.7673 - 0.5948 = 0.1725

(e) less than or equal to 2.3 NM Probability

P(Z ≤ 2.3) = 0.9893

(f) greater than 2.22 NM or less than .65 NM

P(Z > 2.22) = 1 - p(Z < 2.22) = 1 - 0.9868 = 0.0132

P(Z < 0.65) = 0.7422

0.7422 - 0.0132 = 0.729

(g) greater than or equal to 2.0 NM Probability

P(Z ≥2) = 1 - p(Z ≤ 2)

1 - 0.97725 = 0.02275

not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove. 

an inaccurate proof leads to errors, or stating results that are not accurate.  which wil mess the probelm up you dont want this

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1