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
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion indicated. Use the related Z value to solve for the score.
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 properties of the normal distribution.
First, calculate the z-score for the value 22 minutes using the formula:
z = (x - mean) / standard deviation
In this case, the mean is 17 minutes and the standard deviation is 3 minutes:
z = (22 - 17) / 3
z = 5 / 3
z ≈ 1.67
Next, we need to find the probability of a z-score greater than 1.67. This can be done by using a standard normal distribution table or a calculator with a normal distribution function.
Looking up the z-score of 1.67 in the standard normal distribution table, we find that the area under the curve to the left of 1.67 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 approximately 0.9525.
For the additional question about the arrival time in which 10% of all arrival times fall below, we can use the properties of the normal distribution and z-scores.
We want to find the z-score that corresponds to the 10th percentile. In other words, we are looking for the z-score such that the area to the left of it under the standard normal distribution curve is 0.10.
Using a standard normal distribution table or a calculator with a normal distribution function, we can find the z-score that corresponds to a cumulative probability of 0.10 is approximately -1.28.
Now, we can use the z-score formula and solve for x to find the corresponding arrival time:
z = (x - mean) / standard deviation
-1.28 = (x - 17) / 3
Multiply both sides by 3:
-3.84 = x - 17
Add 17 to both sides:
x ≈ 13.16
Therefore, the arrival time in which 10% of all arrival times fall below is approximately 13.16 minutes.
So, the correct answers to the given questions are:
Probability that it will take the medical squad more than 22 minutes: 0.9525
Arrival time in which 10% of all arrival times fall below: 13.16 minutes