A government organization is examining the effectiveness of a program intended to shorten security lines at airports for "trusted travelers". For comparison purposes, a sample was obtained of the time in seconds it took passengers not on the program to pass through security at a certain international airport. The accompanying data contain the results. Complete parts a through c below. A Click the icon to view the security time data. a. Calculate the sample mean and the sample standard deviation for this sample of passenger times. The sample mean is seconds. (Round to two decimal places as needed.) The sample standard deviation is seconds. (Round to two decimal places as needed.) b. Assume that the distribution of time required to pass through security at this airport normally distributed. Use the sample data to construct a 99% confidence interval estimate for the average time required to pass through security. The 99% confidence interval is seconds- seconds. (Round to two decimal places as needed.) Security Time Data c. What is the margin of error for the confidence interval constructed in part b? e=t seconds (Round to two decimal places as needed.) 371 218 147 164 207 370 103 a00
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
All of the sample data is in the two pictures
 alt="A government organization is examining the effectiveness of a program intended to shorten security lines at airports for "trusted travelers". For comparison purposes, a sample was obtained of the time in seconds it took passengers not on the
program to pass through security at a certain international airport. The accompanying data contain the results. Complete parts a through c below.
Click the icon to view the security time data.
a. Calculate the sample mean and the sample standard deviation for this sample of passenger times.
The sample mean is
seconds.
(Round to two decimal places as needed.)
The sample standard deviation is
(Round to two decimal places as needed.)
seconds.
b. Assume that the distribution of time required to pass through security at this airport is normally distributed. Use the sample data to construct a 99% confidence interval estimate for the average time required to pass through security.
The 99% confidence interval is
seconds-
seconds.
(Round to two decimal places as needed.)
Security Time Data
c. What is the margin of error for the confidence interval constructed in part b?
e = +
seconds
(Round to two decimal places as needed.)
371
218
147
164
207
379
192
329
228
208
178
244
288
366
244
371
150
185
288
232
360
388
352
228
142
253
259
299
320
235
124
220
287
302
194
143
175
138
305
244
226
222
407
215
183
313
365
359
297
400
264
239
Enter your answer in each of the answer boxes.
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307
310
245
296
37
424
374
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218
210
326
240
150
243
229
231
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