Normal Probability Distribution
The goal at U.S. airports handling international flights is to clear these flights within 45 minutes. Let's interpret this to mean that 95 percent of the flights are cleared in 45 minutes, so 5 percent of the flights take longer to clear. Let's also assume that the distribution is approximately normal.
a) If the standard deviation of the time to clear an international flight is 5 minutes, what is the mean time to clear a flight?
b)Suppose the standard deviation is 10 minutes, not the 5 minutes suggest in part a) what is the mean?
c) A customer has 30 minutes from the time her flight landed to catch her limousine. Assuming a standard deviation of 10 minutes, what is the likelihood that she will be cleared in time?
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a) If the standard deviation of the time to clear an international flight is 5 minutes, what is the mean time to clear a flight?
M +z*s=45minutes
where M = mean and
z coreesponds to 95%confidence 1 tailed test
or 5.00%level of significance (a (alpha) =0.05)
This is a 1 tailed test because we have the condition that 5 percent of the flights take longer to clear
95 percent of the flights are cleared in 45 minutes, so 5 ...
Solution Summary
Answer to questions on Normal Probability Distribution. It calculates the mean time to clear a flight.
Normal Probability distribution applications
Problem 1)
The weigh of a sophisticated running shoe is normally distributed with a mean of 12 ounces and a standard deviation of 0.5 ounces.
a) What is the probability that a shoe weighs more than 13 ounces?
b) What must the standard deviation of weght be in order for the company to state that 99.9% of its shoes are leass than 13 ounces?
c) If the standard deviation remains at 0.5 ounces, what must the mean weight be in order for the company to state that 99.9% of its shoes are less than 13 ounces?
Problem 2)
The diameter of the dot produced by a printer is normally distributed with a mean diameter of 0.002 inches and a standard deviation of 0.0004 inches.
a) What is the probability that the diameter of a dot exceeds 0.0026?
b) What is the probability that a diameter is between 0.0014 and 0.0026 inches?
c) What standard deviation od diameters is needed so that the probability in part (b) is 0.995?