Respuesta :
Answer: a. The value of the mean is
μ=9 peas
The value of the standard deviation is
σ= 2.6 peas
b. Values of 3.8 peas or fewer are significantly low.
Values of 14.2 peas or fewer are significantly low.
c. The result is significantly low, because 2 peas with green pods is less than 3.8 peas.
Step-by-step explanation:
Given : The probability that a pea has green pods : p=0.25
Sample size : n= 36
a) Then, the mean and the standard deviation for the numbers of peas with green pods in the groups of 36 would be :-
[tex]\mu=np=36(0.25)=9\\\\\sigma=\sqrt{np(1-p)}\\\\=\sqrt{36(0.25)(1-0.25)}\\\\=\sqrt{6.75}\approx2.6[/tex]
Thus , The value of the mean is
μ=9 peas
The value of the standard deviation is
σ= 2.6 peas
b) According to the range rule of thumb :-
Minimum usual value =  μ-2σ
=9-2(2.6) =3.8
⇒Values of 3.8 peas or fewer are significantly low.
Maximum usual value =  μ+2σ
=9+2(2.6) = 14.2
⇒Values of 14.2 peas or fewer are significantly low.
c. Clearly 2 < Minimum usual value (3.8)
⇒The result is significantly low, because 2 peas with green pods is less than 3.8 peas.