The average scuba diver can stay under water for 42 minutes with a standard deviation of 8 minutes, what is the probability that a diver stays under for more than 36 minutes
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To find the probability that a diver stays under water for more than 36 minutes, we can use the concept of the standard normal distribution.
Step 1: Convert the problem to a standard normal distribution.
We need to calculate the z-score for the given value of 36 minutes. The z-score is calculated using the formula: z = (x - μ) / σ, where x is the given value, μ is the mean, and σ is the standard deviation.
In this case, x = 36 minutes, μ = 42 minutes, and σ = 8 minutes.
z = (36 - 42) / 8 = -0.75
Step 2: Find the probability using z-score.
To find the probability of a value more than 36 minutes, we need to find the area under the standard normal curve to the right of the z-score (-0.75). This can be done using a standard normal distribution table or a calculator.
Using a standard normal distribution table, the area to the right of -0.75 is 0.7734.
Step 3: Calculate the probability.
The probability of a diver staying under water for more than 36 minutes is 0.7734 or 77.34%.
Therefore, there is a 77.34% probability that a diver stays under water for more than 36 minutes.