# Qbank Quant Question

Question:- An airline was concerned about passengers arriving too late at the airport to allow for the additional security measures. The airline collected survey data from 1,000 passengers on their time from arrival at the airport to reaching the boarding gate. The sample mean was 1 hour and 20 minutes, with a sample standard deviation of 30 minutes. Based on this sample, how long prior to a flight should a passenger arrive at the airport to have a 95% probability of making it to the gate on time? A) Two hours, thirty minutes. B) One hour, fifty minutes. C) Two hours, ten minutes. Answer in QBank:- We can use standard distribution tables because the sample is so large. From a table of area under a normally distributed curve, the z value corresponding to a 95%, one-tail test is: 1.65. (We use a one-tailed test because we are not concerned with passengers arriving too early, only arriving too late.) Here, we do not divide by the standard error, because we are interested in a point estimate of making our flight. The answer is one hour, twenty minutes + 1.65(30 minutes) = 2 hours, 10 minutes. My Questions:- 1. Why did they use 1.65 instead of 1.96 for 95% confidence? 2. Why was standard deviation used directly and not standard error since we are working with a sample? Did not get the explanation above.

Another One: The probability density function of a continuous uniform distribution is best described by a: A) horizontal line segment. B) line segment with a curvilinear slope. C) line segment with a 45-degree slope. Answer: A) horizontal line segment. Can someone explain?

1. Because it is a one-sided statistical test. You are only interested in excluding the 5% late arrivals, no early arrival. 2. The sample is large enough (i.e. larger than 30) in which case it is considered that the sample is normally distributed (it is proven that samples with many observations tend to basically have the shape of a normal distribution).

I understand the 1st part about the one tailed test, but not about the 2nd part. When do we use standard error and when standard deviation. If you look at the CFAI notebook V1 page 436 example 4, even though the sample size is 100 (>30), it is using the standard error. I am sure I am missing something here. Also, can someone throw some light on the PDF question.

Anyone??

The PDF for a normal curve would be curvilinear but here the key word is “uniform.” A continuous function with a uniform distribution would have the same density at all levels, making it a horizontal line.

Can anyone throw some light on the 1st question? When do we use standard error and when standard deviation. If you look at the CFAI notebook V1 page 436 example 4, even though the sample size is 100 (>30), it is using the standard error. I am sure I am missing something here. Appreciate your help!

search for this same question. I am pretty sure JoeyDVivre had given a very good explanation some time ago… (search with no time bounds) and you will get the answer. This is a JUNK question…

Thanks cpk123, it helps to know it was junk.