Question

Mark noticed that the probability that a certain player hits a home run in a single game is 0.175. Mark is interested in the variability of the number of home runs if this player plays 200 games. If Mark uses the normal approximation of the binomial distribution to model the number of home runs, what is the standard deviation for a total of 200 games? Answer choices are rounded to the hundredths place.

Answer #1

Solution

Let X = number of home runs of this player in 200 games played by him. Then, X ~ B(200, p), where p = probability that a this player hits a home run in a single game and this is given to be 0.175.

Thus, X ~ B(200, 0.175) …………………………………………………………………………… (1)

Back-up Theory

Normal approximation

If X ~ B(n, p) np ≥ 5 and np(1 - p) ≥ 5, (X – np)/√{np(1 - p)} ~ N(0, 1) [approximately] ……… (2)

Where np = Mean of X and √{np(1 - p)} is the standard deviation of X.

Now to work out the solution

Here n = 200 and p = 0.175. So, standard deviation for a total of 200 games is the standard deviation for a total of X

= √{200 x 0.175 x 0.825) [vide (2)]

= **5.3735 Answer**

**DONE**

Mark noticed that the probability that a certain player hits a
home run in a single game is 0.175. Mark is interested in the
variability of the number of home runs if this player plays 200
games.
If Mark uses the normal approximation of the binomial
distribution to model the number of home runs, what is the standard
deviation for a total of 200 games? Answer choices are rounded to
the hundredths place.
5.37
0.14
28.88
5.92

A certain baseball player hits a home run in 7% of his at bats.
Consider his at bats as independent events. Find the probability
that this baseball player hits more than 42 home runs in 800 at
bats.
Please show work.

A certain baseball player hits a home run in 7% of his at-bats.
Consider his at-bats as independent events. Find the probability
that this baseball player hits at most 42 home runs in 800
at-bats?
0.0307
0.9693
0.93
0.07

A certain baseball player hits a home run in 4% of his
at-bats. Consider his at-bats as independent events. Find the
probability that this baseball player hits more than 16 home runs
in 650 at-bats?
0.9713
0.0287
0.96
0.04

A
certain baseball player hits a home run in 7% of his at-bats.
Consider his at-bats as independent events. Find the probability
that this baseball player hits more than 42 home runs in 800
at-bats?
a) 0.93
b) 0.9693
c) 0.07
d) 0.0307

Please answer the following Case
analysis questions
1-How is New Balance performing compared to its primary rivals?
How will the acquisition of Reebok by Adidas impact the structure
of the athletic shoe industry? Is this likely to be favorable or
unfavorable for New Balance?
2- What issues does New Balance management need to address?
3-What recommendations would you make to New Balance Management?
What does New Balance need to do to continue to be successful?
Should management continue to invest...

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