Answer:
a) Standard Deviation = 2.74
b) Significantly Low = values below 24.52 (or equal)
Significantly High = values above 35.48 (or equal)
Step-by-step explanation:
This is binomial probability distribution problem.
Where n = 40 [groups of 40, total trials]
p = 0.75 [probability of success]
a)
The formula for standard deviation is:
[tex]Standard \ Deviation = \sqrt{np(1-p)}[/tex]
We know n = 40 and p = 0.75, so the standard deviation is:
[tex]Standard \ Deviation = \sqrt{np(1-p)} \\Standard \ Deviation = \sqrt{(40)(0.75)(1-0.75)}\\ Standard \ Deviation = 2.74[/tex]
b)
the range rule of thumb tells us that usual range of values is within 2 standard deviation of the mean. First let's calculate mean.
We know,
Mean = n * p = 40 * 0.75 = 30
So
Mean - 2* Standard Deviation = 30 - 2(2.74) = 24.52
and
Mean + 2* Standard Deviation = 30 + 2(2.74) = 35.48
Significantly Low = values below 24.52 (or equal)
Significantly High = values above 35.48 (or equal)
