Download Sta 120 Sp 04 Inst: Wong, D

Math 227 Sp’08 Inst: Wong, D. Ch5 to 6 Test Name: _________________________
#1
For the following probability distribution,
x
P(x)
4pt.
1
0.25
2
0.10
3
4
0.5
(a) Find P( x = 3).
10pt. (c) Find the mean and standard deviation of the distribution.
#2
6pt.
A researcher from a college reported that 72% of single-vehicle traffic fatalities
that occur at night on weekends involve an intoxicated driver. If a sample of 15
single-vehicle traffic fatalities that occur at night on a weekend is selected, use the
Binomial formula to find the probability that exactly 12 involve a driver who is
intoxicated.
#3
6pt.
If 60% of all women are employed outside the home, use the Binomial table to
find the probability that in a sample of 20 women at least 16 are employed outside
of the home.
#4
8pt.
A lottery offers one $1000 prize, one $500 prize, and five $100 prizes. One
thousand tickets are sold at $3 each. Find the expectation (E(x)) if a person
buys one ticket.
#5
4pt.
Assume the z scores are normally distributed with a mean of 0 and a standard
deviation of 1.
a)
Find P(z > -1.58)
4pt.
b)
#6
5pt.
Determine the value of z so that the area under the standard normal curve to
the left of z is 0.0250.
#7
8pt.
IQ scores are normally distributed with a mean of 100 and a standard deviation
of 15. If we define a genius to be someone in the top 1% of IQ scores, find the
score separating geniuses from the rest of us.
Find P( -2.85 < z < -1.07)
#8
Heights of women are normally distributed with a mean of 63.6 in. and a
standard deviation of 2.5 in. (based on data from the National Health Survey).
10pt. If a woman is randomly selected, find the probability that her height is between
60 in. and 69 in.
#9
4pt.
Replacement times for TV sets have a mean of 8.2 years and a standard deviation
of 1.4 years. If 45 TV sets are randomly selected,
a) should the mean replacement time, x , be normally distributed? Explain.
10pt. b) find the probability that x will be greater than 17.2 years.
#10
A history class has 75 students. If there is a 18% absentee rate per class meeting,
4pt.
(a) find the mean and standard deviation of the number of students who will be
absent per class meeting.
9pt.
(b) use a normal distribution to approximate a binomial distribution procedure
to find the probability that among 75 students, there are at most 15 students
who will be absent per class meeting.
#11
2pt.
each
True or False
__________
a) If x is a random variable for a binomial distribution, x is a
discrete random variable.
__________
b) If the population distribution is normally distributed and a
sample size of 20 is randomly selected from the population,
the distribution of the sampling mean x is not guaranteed to
be normally distributed.
__________
c) As n increases,  x decreases.
__________
d) For the standard normal distribution  = 0 and  = 1.