IGNOU MTE 3 2018 - Suppose that the temperature is normally distributed with expectation

Question

Suppose that the temperature is normally distributed with expectation 50o C and variance 4o C . What is the probability that the temperature T will be between 48o C and 53o C ?
What is the probability that T ≥ 52o C ?

02 Feb 2018

Answer :

Word Count : 423

Given that the temperature \( T \) follows a normal distribution with mean \( \mu = 50^\circ C \) and variance \( \sigma^2 = 4 \), the standard deviation \( \sigma \) will be: \[ \sigma = \sqrt{4} = 2 \] Now, let's solve the two parts of the problem. ### 1. Probability that the temperature will be between \( 48^\circ C \) and \( 53^\circ C \). We are asked to find the probability \( P(48 \leq T \leq 53) \). We will first convert the values of \( 48^\circ C \) and \( 53^\circ C \) into their respective \( z \)-scores using the formula: \[ z = \frac{x - \mu}{\sigma} \] For \( x = 48 \): \[ z_1 = \frac{48 - 50}{2} = \frac{-2}{2} = -1 \] For \( x =

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