ls Spring 2015 answer.. 19. Do the multiple choice questions 6.8-6.14 from the t

Question

ls Spring 2015 answer.. 19. Do the multiple choice questions 6.8-6.14 from the textbook. PART II: For the followin questions clearly show all of your work Question 1. Assume that the annual salaries of part-time bank tellers is normally distributed with a mean of $22,500 and a standard deviation of $1,000. (a) What is the probability that the salary of a randomly selected part-time bank teller will be between 822,000 and $23,000? Let x be the salary of a randomly selected part-time bank teller. Then P(22000 x 23000) P(-0,5

Explanation / Answer

Solution:

a) P (22000 < X < 23000) = P ( 22000 - 22500/1000 < X / < 23000 - 22500/1000 )
= P (-0.5 < Z < 0.5)
= P ( Z < 0.5 )P(Z < 0.5 )
= P ( Z < 0.5 )(1P ( Z < 0.5 ))
= 0.6915 - 0.3085 (from the Z score table)
= 0.383

b) Z0.025 = 1.96
X = Z * +
= 1.96 * 1000 + 22500
= 24460

c) X = number of tellers with salaries between $22,000 and $23,000 follows Binomial distri- bution with
N = 30 , p = 0.383,
where np = 11.49 > 5 , nq = 18.51 > 5.
So Normal is appropriate approximation with = 11.49 , 2 = 11.49 * 0.617 = 7.09
P ( X > 10) = P ( Z > 10 - 0.5 - 11.49 7.09
= P ( Z > - 0.75)
= 1 - P ( Z < - 0.75)
= 1 - 0.2266
= 0.7734

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