The time for an emergency medical squad to arrive at the sports center at the edge of a particular town is normally distributed with mean 17 minutes and standard deviation 3 minutes.
What is the probability that it will take the medical squad more than 22 minutes to arrive at the sports center?
0.4525
0.9525
0.0475
0.5475
none of the above
* 23 hours ago
* - 3 days left to answer.
Additional Details
What is the arrival time in which 10% of all arrival times fall below?
13.16
17.00
20.84
16.25
5.48
To find the probability that it will take the medical squad more than 22 minutes to arrive at the sports center, we need to calculate the area under the normal distribution curve to the right of 22 minutes.
First, we need to standardize the value of 22 minutes using the formula: z = (x - μ) / σ, where x is the given value (22 minutes), μ is the mean (17 minutes), and σ is the standard deviation (3 minutes).
z = (22 - 17) / 3 = 5 / 3
Then, we can use a standard normal distribution table or a calculator to find the corresponding probability.
Looking it up in a standard normal distribution table or using a calculator, the z-score corresponds to a probability of approximately 0.9525.
Therefore, the probability that it will take the medical squad more than 22 minutes to arrive at the sports center is 0.9525.
For the additional question, we need to find the arrival time in which 10% of all arrival times fall below, i.e., the value that corresponds to the lower 10th percentile.
Using the standard normal distribution table or a calculator, we find the z-score that corresponds to the lower 10th percentile is approximately -1.28.
Now, we can use the formula z = (x - μ) / σ and solve for x: -1.28 = (x - 17) / 3.
Rearranging the equation, we get: x - 17 = -1.28 * 3.
Simplifying, we find: x - 17 = -3.84.
Adding 17 to both sides, we get: x = 13.16.
Therefore, the arrival time in which 10% of all arrival times fall below is 13.16 minutes.
To find the probability that it will take the medical squad more than 22 minutes to arrive at the sports center, we can use the standard normal distribution.
First, we need to standardize the value 22 minutes using the formula:
Z = (X - μ) / σ
where X is the value, μ is the mean, and σ is the standard deviation.
Let's calculate the standardized value:
Z = (22 - 17) / 3
Z = 5 / 3
Z ≈ 1.67
Now, we can find the probability using a standard normal distribution table or a calculator.
Looking up the value of 1.67 in the standard normal distribution table (or using a calculator), we find that the corresponding cumulative probability is approximately 0.9525.
Therefore, the probability that it will take the medical squad more than 22 minutes to arrive at the sports center is 0.9525.
For the second question, we want to find the arrival time in which 10% of all arrival times fall below. This is equivalent to finding the value with a cumulative probability of 0.10.
Using the standard normal distribution table (or a calculator), we can find the corresponding value.
Let's find this value:
Z = InvNorm(0.10) ≈ -1.28
Now, we can use the formula to calculate the arrival time:
X = (Z * σ) + μ
X = (-1.28 * 3) + 17
X ≈ 13.16
Therefore, the arrival time in which 10% of all arrival times fall below is approximately 13.16 minutes.