The time to fly between New York City and Chicago is normally distributed with a mean of 180 minutes and a standard deviation of 17 minutes. What is the probability that a flight is more than 200 minutes?
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score. Hint: look in the smaller portion.
To find the probability that a flight is more than 200 minutes, we need to calculate the area under the normal distribution curve to the right of 200.
Step 1: Standardize the value of 200 using the formula (X - mean)/standard deviation, where X is the value we want to standardize.
(200 - 180) / 17 = 20 / 17 ≈ 1.176
Step 2: Look up the corresponding area under the standard normal distribution curve for the standardized value. In this case, we need to find the area to the right of 1.176.
Step 3: Using a standard normal distribution table or a calculator, find the area to the left of 1.176. This represents the area under the curve from negative infinity to 1.176.
Step 4: Subtract the obtained area from 1 to get the area to the right of 1.176, which is the probability that a flight is more than 200 minutes.
Calculating this using a standard normal distribution table or a calculator, we find that the area to the left of 1.176 is approximately 0.881.
Subtracting this from 1, we get:
1 - 0.881 ≈ 0.119
Therefore, the probability that a flight is more than 200 minutes is approximately 0.119 or 11.9%.