Question

A thermocouple placed in a certain medium produces readings within 0.1°C of the true temperature 75% of the time, readings more than 0.1°C above the true temperature 5% 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) In a series of 10 independent readings, what is the probability that more than 8 of the readings are within 0.1°C of the true temperature?

Answer 1

a)

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

=(10!/(5!*2!*3!))*(0.75)^3*(0.05)^2*(0.2)^3=0.01196

b)

probability that more than 8 of the readings are within 0.1°C of the true temperature

=P(X=9)+P(X=10)

=(₁₀C₉)*(0.75)⁹*(0.25)¹+(₁₀C₁₀)*(0.75)¹⁰*(0.25)⁰=0.2440