Heights of men on a baseball team have a bell-shaped

Heights of men on a baseball team have a bell-shaped

Heights of men on a baseball team have a bell-shaped

Week 2 Quiz
1.
Heights
of men on a baseball team have a bell-shaped distribution with a mean of 177cm
and a standard deviation of 5cm. Using
the empirical rule, what is the approximate percentage of the men between the
following values?
a)
167cm
and 187cm
b)
162cm
and 192cm
2.
Heights
of women have a bell-shaped distribution with a mean of 163cm and a standard
deviation of 5cm. Using Chebyshev’s
theorem, what do we know about the percentage of women with heights that are
within 3 standard deviations of the mean?
What are the minimum and the maximum heights that are within 3 standard
deviations of the mean?
a)
At
least _____ % of women have heights within 3 standard deviations of 163cm. (Round to the nearest Percent)
b)
The
minimum height that is within 3 standard deviations of the mean is _____ cm.
c)
The
maximum height that is within 3 standard deviations of the mean is _____ cm.
3.
Determine
whether the distribution is a discrete probability distribution:
x P(x)
0
0.28
1
0.32
2
-0.20
3
0.32
4
0.28
Is the probability distribution a
discrete distribution? Why?
Choose the correct answer below:
a)
No,
because some of the probabilities have values greater than 1 or less than 0
b)
No,
because the total probability is not equal to 1
c)
Yes,
because the probabilities sum to 1 and are all between 0 and 1, inclusive.
d)
Yes,
because the distribution is symmetric
4.
In
a state’s Pick 3 lottery game, you pay $1.28 to select the sequence of three
digits, such as 222. If you select the
same sequence of three digits that are drawn, you win and collect $420.17. Complete parts A-E.
a)
How
many different selections are possible?
b)
What
is the probability of winning? _____ (Enter integer or decimal)
c)
If
you win, what is your net profit? (Enter integer or decimal)
d)
Find
the expected value. _____ (Round to the nearest hundredth as needed)
e)
If
you bet $1.28 in a certain state’s Pick 4 game, the expected value is
$0.86. Which bet is better, a $1.28 bet
in the Pick 3 game or a $1.28 bet in the Pick 4 game? Explain.
a.
Neither
bet is better because both games have the same expected value
b.
The
Pick 3 game is a better bet because it has a larger expected value
c.
The
Pick 4 game is a better bet because it has a larger expected value
5.
Assume
that a procedure yields a binomial distribution with a trial repeated n
times. Use a binomial probabilities
table to find the probability of x success given the probability p of success
on a given trial. N=3, x=1, p=0.80
P (1) =
_____ (Round to 3 decimal places as needed)
6.
In
a region, 70% of the population have brown eyes. If 10 people are randomly selected, find the
probability that at least 8 of them have brown eyes. Is it unusual to randomly select 10 people
and find that at least 8 of them have brown eyes? Why or why not?
The probability that at least 8 of the 10 people
selected have brown eyes is _____? (Round to 3 decimal places as needed)
Is it unusual to randomly select 10 people and find
that at least 8 of them have brown eyes?
Note that a small probability is one that is less than 0.05
a)
No,
because the probability of this is occurring is very small.
b)
Yes,
because the probability of this occurring is not small.
c)
Yes,
because the probability of this occurring is very small.
d)
No,
because the probability of this occurring is not small.
7.
Assume
that a procedure yields a binomial distribution with n trials and the
probability of success for one trial is p.
Use the given values of n to find the mean and standard deviation. Also, use the range rule of thumb to find the
minimum value and the maximum value.
n=1540, p=2/5
mean= _____
standard deviation=_____ (Round one
decimal place as needed)
minimum value= _____ (Round one
decimal place as needed)
maximum value= _____ (Round one
decimal place as needed)
8.
A
government agency has specialists who analyze the frequencies of letters of the
alphabet in an attempt to decipher intercepted messages. In Standard English text, a particular letter
is used at a rate of 7.2%.
a)
Find
the mean and standard deviation for the number of times this letter will be
found on a typical page of 1900 characters.
b)
In
an intercepted message, a page of 1900 characters is found to have3 the letter
occurring 169 times. Is this unusual?
a.
Yes,
because 169 is greater than the maximum usual value
b.
Yes,
because 169 is below the minimum usual value
c.
Yes,
because 169 is within the range of usual values
d.
No,
because 169 is within the range of usual values
9.

Identify the properties that make flipping a coin 50 times and keeping
track of heads a binomial experiment.

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