Final answer:
To find the probability of tuning an engine in a given time range, we can use the cumulative distribution function (CDF) of the exponential distribution. This allows us to calculate the probability of the event occurring within a certain time frame based on the mean of the distribution.
Step-by-step explanation:
To answer part (a), we need to find the probability of tuning an engine in 24 minutes or less. Since the time it takes to tune an engine follows an exponential distribution with a mean of 40 minutes, we can use the cumulative distribution function (CDF) of the exponential distribution to find this probability.
The CDF of the exponential distribution is given by P(X ≤ x) = 1 - e^(-x/mean), where X is the random variable representing the time to tune the engine and mean is the mean of the exponential distribution. Plugging in the values, we get P(X ≤ 24) = 1 - e^(-24/40).
To answer part (b), we can again use the CDF of the exponential distribution. The probability of tuning an engine between 36 and 50 minutes can be calculated as P(36 ≤ X ≤ 50) = P(X ≤ 50) - P(X ≤ 36).