Given a random sample size of n = 400 from a probability distribution with P = 0

Question

Given a random sample size of n = 400 from a probability distribution with P = 0.20 do the following. a. Find the probability that the percentage of successes is greater than 0.25 b. Find the probability that the percentage of successes is less than 0.15. c. Find the probability that the percentage of successes is between 0.17 and 0.24 d. With probability 0.15, the percentage of successes is less than what percent? e. With probability 0.11, the percentage of successes is greater than what percent?

Explanation / Answer

5.43.

a).

standard error = sqrt(p*(1-p)/n) =sqrt(0.20*0.80/400) =0.02

z value for 0.25, z=(0.25-0.20)/0.02 =2.5

P( P>0.25) = P( z > 2.5) =0.0062

b).

z value for 0.15, z=(0.15-0.20)/0.02 =-2.5

P( P<0.15) = P( z < - 2.5) =0.0062

c).

z value for 0.17, z=(0.17-0.20)/0.02 =-1.5

z value for 0.24, z=(0.24-0.20)/0.02 =2.0

P( 0.17<P<0.24) = P( -1.5<z<2.0)=P( z <2.0 )–P(z < -1.5)

= 0.9772- 0.0668

=0.9104

d).

z value for lower side p of 0.15 is -1.036

P =0.20-0.02*1.036=0.17928

The required percentage = 17.93%

e).

z value for upper side p of 0.11 is 1.227

P =0.20+0.02*1.227=0.22454

The required percentage = 22.45%

Related Questions

Navigate

• Browse (All)
• Browse G
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.