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Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 4.4 - Problem 16e
Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 4.4 - Problem 16e

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# A thermocouple placed in a certain medium produces ISBN: 9780073401331 38

## Solution for problem 16E Chapter 4.4

Statistics for Engineers and Scientists | 4th Edition

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Problem 16E

Problem 16E

A thermocouple placed in a certain medium produces readings within 0.1°C of the true temperature 70% of the time, readings more than 0.1°C above the true temperature 10% of the time, and readings more than 0.1°C below the true temperature 20% of the time.

a. In a series of 10 independent readings, what is the probability that 5 are within 0.1°C of the true temperature, 2 are more than 0.1 °C above, and 3 are more than 0.1 °C below?

b. What is the probability that more than 8 of the readings are within 0.1°C of the true temperature?

Step-by-Step Solution:

Solution :

Step 1 of 2:

Let denotes the number of readings.

Let is the readings within 0.10C of the true temperature 70% of the time.

So .

Let is the readings more than 0.10C above the true temperature 10% of the time.

So and

Let is the readings more than 0.10C below the true temperature 20% of the time.

So .

The total number of readings is 10.

Therefore  MN(10,0.70,0.10,0.20)

Our goal is :

a). We need to find the probability that 5 are within 0.10C of the true temperature,

2 are more than 0.10C above and 3 are more than 0.10C below.

b). We need to find the probability that more than 8 of the readings are within  0.10C of the true

temperature.

a).

Now we have to find the probability that 5 are within 0.10C of the true temperature,

2 are more than 0.10C above and 3 are more than 0.10C below.

The multinomial probability formula is given by

P=  We consider , and .

Then,

P( , , =  P( , , = (0.16807) (0.01) (0.003)

P( , , =  0.00000134456

P( , , =2520 0.0000134456

P( , , =0.0338

Therefore P( , , is 0.0338.

Step 2 of 2

##### ISBN: 9780073401331

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