Suppose X is a normal distribution with N(210, 32). Find the following: a. P( X < 230) b. P(180 < X < 245) c. P( X >190) d. Find c such that P( X < c) = 0.0344 e. Find c such that P( X > c) = 0.7486

(a) The value of P (X < 230) is 0.9998.

(b) The value of P (180 < X < 245) is 1.

(c) The value of P (X > 190) is 0.9998.

(d) The value of c is 199.7.

(e) The value of c is 213.79.

Step-by-step explanation:

It is provided that random variable X follows a Normal distribution with parameters μ = 210 and σ = √32.

(a)

Compute the probability of the event X < 230 as follows:

*Use the z-table for the probability.

Thus, the value of P (X < 230) is 0.9998.

(b)

Compute the probability of the event 180 < X < 245 as follows:

*Use the z-table for the probability.

Thus, the value of P (180 < X < 245) is 1.

(c)

Compute the probability of the event X > 190 as follows:

*Use the z-table for the probability.

Thus, the value of P (X > 190) is 0.9998.

(d)

It is provided that P (X < c) = 0.0344.

The value of z for which P (Z < z) = 0.0344 is -1.82.

Compute the value of c as follows:

Thus, the value of c is 199.7.

(e)

It is provided that P (X > c) = 0.7486.

The value of z for which P (Z < z) = 0.2514 is 0.67.

Compute the value of c as follows:

Thus, the value of c is 213.79.

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