Now let’s look at the solutions for the exercises.

Exercise 1 Solution

This can be calculated as follows:

Z = X-μ

     σ /√n

= 74-70   = 4/2 = 2.00 . From the tables the value of z from the table is 0.023 or 2.3%.

  10/ √25

Thus, out of the 25 random samples, 2.3%  is expected to have a mean heart rate of 74 beats per minute or

higher.

Exercise 2. Solution

To find the solution we need to look at the normal curve and find the value of the mean. For this we need to look at z value that divides the upper 5% from lower  95%, which is 0.05. And when we look this up in the tables the value is 1.645. By substituting this value in the formula:

Z = X-μ

     σ /√n

1.645 = X-70

          10/√25

1.645 x2 +70= X

=3.29 +70

Therefore, X = 73.29

Hence, 73.29 is the value that divides the upper 5% from the lower 95% of the sampling distribution.

And there is cause for concern if the mean value of the 25 samples passes this value.