Given:
The area model for .
To find:
The value of and the missing values in the area model.
Solution:
2.1 can be written as 2 and 0.1 on the left side of the area model.
3.2 can be written as 3 and 0.2 on the top of area model.
Area of the four parts of the area model are:
The complete area model is shown below.
After adding all areas of the area model, we get
Therefore, the value of is 6.72 and the missing values of the area model are 0.3 and 0.02 respectively.
Answer:
a
b
Step-by-step explanation:
From the question we are told that
The mean value is
The standard deviation is
Considering question a
The sample size is n = 9
Generally the standard error of the mean is mathematically represented as
=>
=>
Generally the probability that the sample mean hardness for a random sample of 9 pins is at least 51 is mathematically represented as
=>
From the z table the area under the normal curve to the left corresponding to 2.5 is
=>
=>
Considering question b
The sample size is n = 40
Generally the standard error of the mean is mathematically represented as
=>
=>
Generally the (approximate) probability that the sample mean hardness for a random sample of 40 pins is at least 51 is mathematically represented as
=>
=>
From the z table the area under the normal curve to the left corresponding to 5.2715 and
=>
So
=>