ECO 578 SPRING 201 XXXXXXXXXXPage 1 of 18 Exam II  Work Problems from page(1 to 18): **All formula and work must be shown step by step and graphs need to be drawn.** ** Answers needs to be written in...

ECO 578 SPRING 201 XXXXXXXXXXPage 1 of 18
Exam II
 Work Problems from page(1 to 18):

**All formula and work must be shown step by step and graphs need to be drawn.**

** Answers needs to be written in the space provided in the box.**

 Two different ways to submit your answer sheet
1. Scan your answer sheet and place it in ONE FILE at drop-box. (preferable)
2. Use MS-Word and place it in a drop-box.
**To avoid penalty do not change the order of your answers and upload only one file
**Excel is not acceptable for this test
**Deadline: Tuesday, April 2, 2019 by 1:00 P.M. (CST)
XXXXXXXXXXName: _______________________
XXXXXXXXXXCWID: ________________________
Exam II
Answer the following questions (1-20):

1) Determine the following probabilities:
a) P(?3)
) P(?3 ∩ ?2)
c) P(?1 ∪ ?2|?3)
d) P(?1 ∪ ?3|?2)
e) P(?1|?1 ∪ ?2)
f) P(?1|?3)
g) Are events ?1 ??? ?1 independent? Why or why not ?
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a)
)
ECO 578 SPRING 201 XXXXXXXXXXPage 2 of 18
c)
d)
e)
f)
g)
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2) Determine the following probabilities by using of the table of binomial probabilities:
a) P(X=3|n=50, p=0.10)
) P(X≤5|n=10, p=0.20)
c) P(X>12|n=50, p=0.30)
d) P(X=9|n=20, p=0.80)
a)
)
c)
d)
3) Let X be a binomial random variable with p = 0.7
a) For n = 3, find P(X=1)
) For n = 5, find P(X≤3)
a)
)
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4) Twenty trials are conducted in a Bernoulli process in which the probability of success in a
given trial is 0.6. If X = the number of success, determine the following:
a) E(X)
) ??
c) P(X=4)
d) P(2≤X≤6)
e) P(X>5)
a)
)
c)
d)
e)
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5) Using the normal distribution, calculate the following probabilities:
a) P(X≤16|n=50, p=0.70)
) P(10≤X≤16|n=50, p=0.50)
a)
)
6) Calculate the following quantities:
a)
4!
2!2!

)
6!
3!3!

c)
7!
5!2!

d)
6!
2!4!

a)
)
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c)
d)
7) Determine the expected value, the variance, and the standard deviation of the following
discrete distribution:
x P[X=x]
1 0.326
2 0.214
3 0.115
4 0.304
5 0.041
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8) What is the difference between the discrete random variable and the continuous random
variable? Please explain.
9) Find the ?? score:
a) P(?≥?0)=0.5
) P(?>?0)=0.9808
c) P(?≥?0)=0.025
d) P(?e) P(?≤?0)=0.025
f) P(-?0g) P(?≥?0)=0.0228
h) P(-?0i) P(0≤?≤?0)=0.4803
j) P(-?0k) P(?l) P(-?0a)
)
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c)
d)
e)
f)
g)
h)
I)
j)
k)
l)
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10) Find each of the following probabilities:
a) P(Z≤1.86)
) P(-1.68≤Z≤0.85)
c) P(Z≥2.77)
d) P(-1.96≤Z≤-1.12)
e) P(Z≤-3.05)
f) P(-1.45≤Z≤1.45)
a)
)
c)
d)
e)
f)
ECO 578 SPRING 201 XXXXXXXXXXPage 10 of 18
11) A random variable x is normally distributed with µ=22 and σ=5. Determine the distance,
in units of standard deviations, between each of the following values of x and mean.
a) x=10
) x=20
c) x=25
d) x=30
e) x=0
f) x=60
a)
)
c)
d)
e)
f)
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12) Find the table values for the following Z scores:
a) Z=2.34
) Z=1.64
c) Z=0.81
d) Z=-2.93
a)
)
c)
d)
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13) Find the Z scores for the following normal distribution.
a) µ=604, σ=56.8, X≤635
) µ=48, σ=12, X<20
c) µ=111, σ=33.8, 100≤X≤150
d) µ=264, σ=10.9, 250e) µ=37, σ=4.35, X<35
f) µ=156, σ=11.4, X≤170
a)
)
c)
d)
e)
f)
ECO 578 SPRING 201 XXXXXXXXXXPage 13 of 18
14) Find ?? from the following probabilities: if µ=160, σ=16
a) P(X>x0) =0.8770
) P(Xc) P(Xd) P(136≤X≤x0) =0.4808
e) P(x0≤X≤204) =0.8185
f) P(180≤X≤x0) =0.0919
a)
)
c)
d)
e)
f)
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15) Assume that x is a binominal random variable with n=100 and p=0.40. Use a normal
approximation to find the following:
a) P(x≥38)
) P(x=45)
c) P(x>45)
d) P(x<45)
a)
)
c)
d)
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16) Work the following binomial distribution problem by using the normal distribution to get
probabilities:
a) P(x=12|n=20 and p=0.40)
) P(x<27|n=100 and p=0.37)
a)
)
17) According to a survey by the U.S. Bureau of Labor statistics, 87% of all the part-time
college students also work. If this figure still holds and if 100 part-time college students
are randomly selected, what is the probabilities that less than 70 part-time college
students also work?
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18) Given a normally distributed population, a sampling distribution is summarized by µ=50,
n=100 and σ=15. What is probabilities that a simple random will reveal a sample mean?
a) P(X̅>63)
) P(53c) P(40d) P(X̅<30)
a)
)
c)
d)
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19) A sample of size n=20 is randomly selected from a normal population with mean µ = 90
and standard deviation σ = 5. Find the following:
a) P(X̅>95)
) P(82c) P(X̅<93)
d) P(X̅<89)
a)
)
c)
d)
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20) Please explain the central limit theory.

practice-dnpgwcl0.pdf