he taxi and takeoff time for commercial jets is a random variable x with a mean of 8.3 minutes and a standard deviation of 3.5 minutes. Assume that the distribution of taxi and takeoff times is approximately normal. You may assume that the jets are lined up on a runway so that one taxies and takes off immediately after the other, and that they take off one at a time on a given runway.
A button hyperlink to the SALT program that reads: Use SALT.
(a) What is the probability that for 35 jets on a given runway, total taxi and takeoff time will be less than 320 minutes? (Round your answer to four decimal places.)
(b) What is the probability that for 35 jets on a given runway, total taxi and takeoff time will be more than 275 minutes? (Round your answer to four decimal places.)
(c) What is the probability that for 35 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes? (Round your answer to four decimal places.)
To solve these probability questions, we need to use the concept of the standard normal distribution. The standard normal distribution is a special case of the normal distribution where the mean is 0 and the standard deviation is 1.
(a) To find the probability that the total taxi and takeoff time for 35 jets will be less than 320 minutes, we first need to standardize the value of 320 using the formula:
Z = (X - mean) / standard deviation
In this case, the mean is 8.3 minutes and the standard deviation is 3.5 minutes. Plugging in the values:
Z = (320 - 8.3) / 3.5
Once we have the standardized value, we can use a standard normal distribution table or a statistical software tool such as the SALT program mentioned in the question to find the corresponding probability. The SALT program can help us with this calculation. By clicking on the provided hyperlink, you can input the value calculated for Z and obtain the probability.
(b) Similarly, to find the probability that the total taxi and takeoff time for 35 jets will be more than 275 minutes, we apply the same standardization formula:
Z = (X - mean) / standard deviation
Using the given values:
Z = (275 - 8.3) / 3.5
Again, we can use the SALT program or a standard normal distribution table to find the corresponding probability.
(c) To find the probability that the total taxi and takeoff time for 35 jets will be between 275 and 320 minutes, we can subtract the probability from part (b) calculated above from the probability from part (a). This is because the probability of an event occurring between two values is equal to the probability of it occurring below the upper value minus the probability of it occurring below the lower value.
P(275 < X < 320) = P(X < 320) - P(X < 275)
Again, we can use the SALT program or a standard normal distribution table to find the corresponding probabilities and subtract them to obtain the final probability.
I hope this explanation helps in understanding how to solve these probability questions.
dbrhnll8
Z = (score-mean)/(SD/√n)
Look up percentages on the Z table in your text.