nt 3 Question 24 (of 35) 2000 points uppose that a large international corporati

Question

nt 3 Question 24 (of 35) 2000 points uppose that a large international corporation wishes to obtain its own benchmark for one-day travel in Moscow. To do this, it records the one-day travel expenses for a random sample of 35 s visiting Moscow. The mean and the standard deviation of these expenses are calculated to be R $535 and s m $45, respectively. Furthermore, a histogram shows that the expenses are approximately distributed, a. Find an interval that you estimate contains 99.73 percent of all one-day travel expenses in Moscow, Interval b. an executive submits an expense of $640 for a one-day stay in Moscow, should this expense be oonsidered unusually high? (Click to seNct Yes

Explanation / Answer

Given that the mean (u) of a normal probability distribution is 500 and the
standard deviation (sd) is 10                  
a.
About 68% of the area under the normal curve is within one standard deviation of the mean. i.e. (u ± 1s.d)
So to the given normal distribution about 68% of the observations lie in between
= [500 ± 10]
= [ 500 - 10 , 500 + 10]
= [ 490 , 510 ]                  
b.
About 95% of the area under the normal curve is within two standard deviation of the mean. i.e. (u ± 2s.d)
So to the given normal distribution about 95% of the observations lie in between
= [500 ± 2 * 10]
= [ 500 - 2 * 10 , 500 + 2* 10]
= [ 480 , 520 ]                  
c.
About 99.7% of the area under the normal curve is within two standard deviation of the mean. i.e. (u ± 3s.d)
So to the given normal distribution about 95% of the observations lie in between
= [500 ± 3 * 10]
= [ 500 - 3 * 10 , 500 + 3* 10]
= [ 470 , 530 ]                  

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