Draw a sketch of the distribution. Then, find the percentage of yogurt tubs that weigh less than 0.88 pounds.
480
Practice makes perfect
We are told that in a sample of yogurt tubs the weights of the yogurts are normally distributed with a mean of 1.0 pound and a standard deviation of 0.06 pounds. Also, we are told that 12 of the tubs weigh less than 0.88 pounds. We want to find the total number of yogurt tubs in the sample.
Number of yougurt tubs=?
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
1-3( 0.06)
1-2( 0.06)
1- 0.06
1.0
1+ 0.06
1+2( 0.06)
1+3( 0.06)
Simplify
0.82
0.88
0.94
1.0
1.06
1.12
1.18
Now, let's draw vertical lines with 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, 1.
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 weights that are less than 0.88 pounds.
We can see that 2.35 %+ 0.15 %=2.5 % of the yogurt tubs weigh less than 0.88 pounds. Also, we know that 12 of the yogurt tubs weigh less than 0.88 pounds. Therefore, 2.5 % of all the yogurt tubs is 12.
2.5 % * Number of yogurts=12 ⇕
Number of yogurts=12/2.5 %
Let's evaluate the number of yogurts!
