Question

Suppose the reaction temperature X (in deg C) in a certainchemical process has uniform distribution with A= -5 and B=5.

a. Compute P(X<0)

b. Compute P(-2.5<X<2.5)

c. Compute P(-2<X<3)

for k satisfying -5<k<k+4<5, computeP(k<X<k+4)

Answer 1

Concepts and reason

The uniform distribution is a probability distribution that has equal probabilities for all possible outcomes of the random variable and the total area under the uniform probability density function is 1. The distribution is often abbreviated as

Fundamentals

The density function of uniform distribution is,

Here,

The lower value of the interval

The upper value of the interval

The cumulative distributed function is,

(a)

From the given information,

So

The density function of X is,

Calculate the probability reaction temperature is less than 0.

Hence, the required probability is,

(b)

Calculate the probability of reaction temperature in a certain chemical process is

Hence, the required probability is,

(c)

Calculate the probability of reaction temperature in a certain chemical process is

Hence, the required probability is,

Calculate the probability of reaction temperature in a certain chemical process is

The value 0.4 satifying the given condition

Hence, the required probability value is

Ans: Part a

The probability of reaction temperature less than 0 is 0.5.

Part b

The probability of reaction temperature in a certain chemical process between -2.5 and 2.5 is 0.5

Part c

The probability of reaction temperature in a certain chemical process lies between -2 and 3 is 0.5

The probability of X lies between k and k+4 is 0.40