Question

Please show all your work and please answer all the questions. It is greatly appreciated with a thumbs up. Thank you!

11. Calculate the Binomial mean if n=40, and q= 0.73.

12. Calculate the Binomial standard deviation if n=36 and 'p=0.45.

13. Basketball player Darby Missalot makes a free throw 75% of the time. What are the chances he will sink his first basket on the 3rd or 4th attempt?

14. The average number of speeding tickets written per year on Main Street is 60. Use the Poisson Formula to determine the chances that 4 tickets will be written on Main Street October.

15. Use the Poisson Table to determine P(x) if x=8 and μ = 8.9.

16. Find the probability P(65 < x < 75), if the mean is 72 and the standard deviation is 2.

17. Use the Standard normal table to find the z-sσcore that corresponds to P88.

18. Calculate x if the mean is 82, the standard deviation is 2 and z=1.28.

19. Determine σ sub x-bar and μ sub x-bar if μ=244, σ=18, and n=9.

20. If n=10, p=0.65 and q=0.35 can you use the normal approximation to the Binomial? If not, why not? Show the math to defend your answer.

Answer 1

#11.
mean = n*p = 40*(1-0.27) = 29.2000

#12.
std. dev. = sqrt(npq) = sqrt(36*0.55*0.45) = 2.9850

#13.
required probability = (1-0.75)^2*0.75 + (1-0.75)^3*0.75 = 0.0586

#14.
P(X = x) = (e^-λ) (λ^x) / x!
P(X = 4) = (e^-60)*(60^4)/4! = 0.0000

#15.
P(X = 8) = (e^-8.9)*(8.9^8)/8! = 0.1332

#16.
P(65 < x < 75) = P(X < 75) - P(x < 65)
= P(z < (75 - 72)/2) - P(z < (65 - 72)/2)
= P(z < 1.5) - P(z < -3.5)
= 0.9330

#17.
z-score = 1.1750

#18.
x = 82 + 1.28*2 = 84.5600

#19.
mu(xbar) = 244
sigma(xbar) = 18/sqrt(9) = 6

#20.
np = 6.5
nq = 3.5
No can not use normal approximation because nq < 5