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
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 related to your Z score.
Reverse the process for the next problem.
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.
Let's use the z-score formula to standardize the value for 22 minutes. The z-score formula is (x - mean) / standard deviation.
z = (22 - 17) / 3
z = 5 / 3
z = 1.67
Next, we need to find the probability associated with the z-score of 1.67. We can find this probability using a standard normal distribution table or a calculator.
Using a standard normal distribution table, we find that the probability of having a z-score greater than 1.67 is approximately 0.0475.
Therefore, the answer to the first question is 0.0475.
To find the arrival time in which 10% of all arrival times fall below, we need to find the z-score that corresponds to the 10th percentile.
Let's call this z-score as z1. The area to the left of z1 is 10%.
Using a standard normal distribution table, we find that the z-score corresponding to the 10th percentile is approximately -1.28.
Next, we can use the z-score formula to find the actual arrival time.
z1 = (x - mean) / standard deviation
-1.28 = (x - 17) / 3
Solving for x:
-1.28 * 3 = x - 17
-3.84 = x - 17
x = 17 - 3.84
x = 13.16
Therefore, the arrival time in which 10% of all arrival times fall below is approximately 13.16 minutes.
The answers are:
For the probability that it will take the medical squad more than 22 minutes to arrive at the sports center: 0.0475
For the arrival time in which 10% of all arrival times fall below: 13.16