The temperature readings from a thermocouple in a furnace fluctuate according to a cumulative distribution function, 0, x < 800 oC
F(x) = 0.05x - 40, 800 oC< or is equal to x < 820 oC
1, x > 820 oC
Determine the following.
A) P(X< 810.0).
B) P(800 C) P(X> 808.40).
D) If the specifications for the process require that the furnace temperature be between 805.60 and 808.40oC, what is the probability that the furnace will operate outside of the specifications?

Step-by-step explanation:

Given:

Solving (a): P(x < 810)

To solve this, we make use of:

Because

So:

Hence:

Solving (b): P(x < 800)

To solve this, we make use of:

Because:

So:

Solving (c): P(x > 808.40)

Here, we make use of complement rule:

Where:

So:

Solving (d) The probability that the temperature lies outside 805.60 and 808.40

First, we calculate the probability that it lies within.

This is represented as:

This is calculated using:

Using complement rule, the required probability is:

72 is the answer to this problem

80 the answer is 80

step-by-step explanation: