Sketch a graph of the distribution. The graph is a bell-shaped normal curve and the highest point of the curve is at the mean.
32 %
Practice makes perfect
We are told that the numbers of paper clips per box in a truckload of boxes are normally distributed with a mean m= 100 and a standard deviation s= 5. To find the probability that a box will not contain between 95 and 100 clips, we will first draw a normal curve. Let's first find the lengths that are one, two, and three standard deviations s away from the mean m.
m-3s
m-2s
m-s
m
m+s
m+2s
m+3s
Substitute
100-3( 5)
100-2( 5)
100- 5
100
100+ 5
100+2( 5)
100+3( 5)
Simplify
85
90
95
100
105
110
115
Now, let's draw vertical lines at these values. Each vertical line will be labeled with the number of standard deviations s it is away from the mean m.
Now we can sketch the normal curve. Let's draw a bell-shaped curve with its highest point at the mean, 100.
The normal curve is divided into sections of standard deviation widths. Let's label the percentages of each section.
Now we will highlight the parts of the graph that are not between 95 and 105 clips.
We can see that only the boxes in the middle 34 %+34 %=68 % contain between 95 and 105 clips. Therefore, the probability that a box will not contain between 95 and 105 clips is equal to 100 % - 68 %.
Probability=100 % - 68 %=32 %
The probability that a box will not contain between 95 and 105 clips is 32 %.
