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 day. Round 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:
Z = (X - μ) / σ
Where:
X = number of kayaks rented out each day = 42
μ = average number of kayaks rented out each day = 42
σ = standard deviation = 4
We can calculate the Z-score as follows:
Z = (42 - 42) / 4
Z = 0 / 4
Z = 0
Next, we can use a Z-table or a calculator to find the probability that Z is less than or equal to 0. The probability is 0.5000.
Therefore, the probability that the company will have enough kayaks on any given day is 0.5 or 50%.
is this right?
Apologies for the confusion in my previous response. Let's correct the calculation.
Given:
- X = number of kayaks rented out each day = 42
- μ = average number of kayaks rented out each day = 42
- σ = standard deviation = 4
- Total number of kayaks available = 45
We want to find the probability that the company will have enough kayaks on any given day, i.e., that they will not run out of kayaks.
To do this, we'll calculate the Z-score using the formula:
Z = (X - μ) / σ
Z = (42 - 42) / 4
Z = 0 / 4
Z = 0
Next, we need to find the probability of having enough kayaks available using the Z-score. For this, we'll find the probability that Z is greater than or equal to 0, as it represents the probability of having enough kayaks.
Using a Z-table or a calculator, you'll find that the probability is approximately 0.5 or 50%.
Therefore, the corrected probability that the company will have enough kayaks on any given day is indeed 0.5 or 50%.