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The risk of females experiencing an anxiety disorder during a given 12-month period is approximately 1...

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Statistics

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

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

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

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

If 20 females are randomly sampled, what is the probability that5 or 6 will experience an anxiety disorder? (Round answer to 3decimal places)

If 10 females are randomly sampled, what is the probability that5 or more will experience an anxiety disorder? (Round answer to 3decimal places)

Answer & Explanation Solved by verified expert
3.7 Ratings (705 Votes)

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
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