A laboratory worker finds that 1.8% of his blood samples test positive for the HIV virus.If 270 blood samples are selected at random,is it appropriate to use a normal model to approximate the distribution of the number that test positive for the HIV virus?
A)Yes;normal model with μ = 4.86 and σ = 4.77 can be used to approximate the distribution
B)No;normal model cannot be used to approximate the distribution because nq

Question

A laboratory worker finds that 1.8% of his blood samples test positive for the HIV virus.If 270 blood samples are selected at random,is it appropriate to use a normal model to approximate the distribution of the number that test positive for the HIV virus?
A)Yes;normal model with μ = 4.86 and σ = 4.77 can be used to approximate the distribution
B)No;normal model cannot be used to approximate the distribution because nq < 10
C)Yes;normal model with μ = 4.86 and σ = 2.18 can be used to approximate the distribution
D)No;normal model cannot be used to approximate the distribution because np < 10
E)Yes;normal model with μ = 265.14 and σ = 2.18 can be used to approximate the distribution

Quizplus · Accepted Answer

The normal model can be used to approximate the distribution of the number of blood samples that test positive for the HIV virus only if np and n(1-p) are both greater than or equal to 10. 
Here, p = 0.018 (given), and n = 270. 
np = 270*0.018 = 4.86, which is less than 10. Hence, we cannot use the normal model to approximate the distribution in this case. 
Therefore, the correct option is (D).

A Laboratory Worker Finds That 1