We are told that a daily airline flight has a mean of 380 checked pieces of luggage and a standard deviation of 20. We are asked to find for what percentage of the flights we should expect from 340 to 420 pieces of checked luggage.
Percentage of flights=?
To do that we will make a graph of the distribution. First, let's find the values that are one, two, and three standard deviations away from the mean. For convenience, the mean will be represented by the letter m and the standard deviation will be represented by s.
m-3s
m-2s
m-s
m
m+s
m+2s
m+3s
Substitute
380-3( 20)
380-2( 20)
380- 20
380
380+ 20
380+2( 20)
380+3( 20)
Simplify
320
340
360
380
400
420
440
Now, let's draw vertical lines with the calculated values.
Now we are ready to sketch the normal curve. Let's draw a bell-shaped curve with its highest point at the mean, 380.
The normal curve is divided into sections of standard deviation widths. Let's label the percentages of each section.
Let's highlight the parts of the graph that represent the flights with 340-420 checked pieces of luggage.
Let's add up the highlighted percentages.
13.5 %+34 %+34 %+13.5 %=95 %
We found that 95 % of the flights check between 340 and 420 pieces of luggage. This result corresponds with option D.
