Final answer:
To find the probability that the drone will fly less than 4.66 hours, calculate the z-score and look up the corresponding probability in the standard normal distribution. A z-score of -2.5 indicates a probability of about 0.62%.
Step-by-step explanation:
To calculate the probability that the drone will fly less than 4.66 hours, we need to convert the flight time of 4.66 hours into a z-score. The z-score represents how many standard deviations an element is from the mean.
The formula to calculate the z-score is:
Z = (X - μ) / σ
Where:
X = Value we're interested in (4.66 hours)
μ = Mean (4.76 hours)
σ = Standard deviation (0.04 hours)
Calculating the z-score:
Z = (4.66 - 4.76) / 0.04 = -2.5
Now, we look up the z-score in the standard normal distribution table or use a calculator to find the probability to the left of that z-score, which gives us the probability that the drone will fly less than 4.66 hours. Typically, a z-score of -2.5 corresponds to a probability of approximately 0.0062 or 0.62%.
Therefore, the probability that the drone will fly less than 4.66 hours is about 0.62%.