Question

The risk of females experiencing an anxiety disorder during a given 12-month period is approximately 1 in 5. Suppose a researcher plans to take a random sample of females and monitor their anxiety over 12 months.

If 20 females are randomly sampled, what is the probability that exactly 10 will experience an anxiety disorder during this 12-month period? (Round answer to 3 decimal places)

If 20 females are randomly sampled, what is the probability that exactly 5 will experience an anxiety disorder? (Round answer to 3 decimal places)  

If 30 females are randomly sampled, what is the probability that exactly 5 will experience an anxiety disorder? (Round answer to 3 decimal places)  

If 20 females are randomly sampled, what is the probability that 5 or 6 will experience an anxiety disorder? (Round answer to 3 decimal places)

If 10 females are randomly sampled, what is the probability that 5 or more will experience an anxiety disorder? (Round answer to 3 decimal places)

Answer 1

1)

here this is binomial with parameter n=20 and p=0.2

probability that exactly 10 will experience an anxiety disorder during this 12-month period:

P(X=10)=

(nCx)px(1−p)(n-x)    =

0.002

2)

If 20 females are randomly sampled, what is the probability that exactly 5 will experience an anxiety disorder

P(X=5)=

(nCx)px(1−p)(n-x)    =

0.175

3)

If 30 females are randomly sampled, what is the probability that exactly 5 will experience an anxiety disorder

P(X=5)=

(nCx)px(1−p)(n-x)    =

0.172

4)

if 20 females are randomly sampled, what is the probability that 5 or 6 will experience an anxiety disorder

P(5<=X<=6)=

∑x=ab     (nCx)px(1−p)(n-x)    =

0.284

5)

If 10 females are randomly sampled, what is the probability that 5 or more will experience an anxiety disorder

P(X>=5)=1-P(X<=4)=

1-∑x=0x-1   (nCx)px(q)(n-x) =

0.033