A kayak-rental company needs to replace many of its kayaks, and it wants to ensure it has enough kayaks to meet the demand from customers during the summer season. On average, it rents out 42 kayaks each day with a standard deviation of 4. The company has 45 kayaks. Use a calculator or spreadsheet program to find the probability that the company will have enough kayaks on any given dayRound the answer to the nearest tenth.
To find the probability that the company will have enough kayaks on any given day, we can use the Z-score formula and the standard normal distribution.
Z = (X - μ) / σ
Where:
X = number of kayaks rented out each day = 42
μ = mean number of kayaks rented out each day = 42
σ = standard deviation of the number of kayaks rented out each day = 4
Z = (42 - 42) / 4 = 0
Now, we can look up the Z-score of 0 in a standard normal distribution table, which will give us the probability of the company having enough kayaks on any given day.
The Z-score of 0 corresponds to a probability of 0.5000.
Therefore, the probability that the company will have enough kayaks on any given day is 0.5, or 50%.