Final answer:
To find the probability that a random variable will assume a value between 60 and 120, calculate the cumulative probability of the random variable being less than or equal to 120 and subtract the cumulative probability of the random variable being less than or equal to 60.
Step-by-step explanation:
The probability that a random variable will assume a value between 60 and 120 can be found by calculating the cumulative probability of the random variable being less than or equal to 120 and subtracting the cumulative probability of the random variable being less than or equal to 60. Let's assume the random variable follows a normal distribution with mean µ and standard deviation σ.
Using the cumulative density function (CDF) of the normal distribution, we can calculate the probabilities P(X ≤ 120) and P(X ≤ 60) and then subtract them to find the probability that the random variable will assume a value between 60 and 120.
P(X ≤ 120) = Φ((120-µ)/σ)
P(X ≤ 60) = Φ((60-µ)/σ)
Probability of the random variable assuming a value between 60 and 120 = P(X ≤ 120) - P(X ≤ 60).