## 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 Chebyshevâs

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 stateâs 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 stateâs 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.

&

What does it mean for the trials to be independent in a binomial

experiment?

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