Batting average A baseball player’s batting average is determined by dividing the number of hits by the number of times at bat and multiplying by 1000. (Batting averages are usually, but not necessarily, rounded to the nearest whole number.) For instance, if a player gets 2 hits in 5 times at bat, his batting average is 400 : ( 2 5 × 1000 = 400 ) . Partway through the season, a player thinks to himself, “If I get a hit in my next time at bat, my average will go up to 250; if I don’t get a hit, it will drop to 187.5.” How many times has this player batted, how many hits has he had, and what is his current batting average?
Batting average A baseball player’s batting average is determined by dividing the number of hits by the number of times at bat and multiplying by 1000. (Batting averages are usually, but not necessarily, rounded to the nearest whole number.) For instance, if a player gets 2 hits in 5 times at bat, his batting average is 400 : ( 2 5 × 1000 = 400 ) . Partway through the season, a player thinks to himself, “If I get a hit in my next time at bat, my average will go up to 250; if I don’t get a hit, it will drop to 187.5.” How many times has this player batted, how many hits has he had, and what is his current batting average?
Solution Summary: The author calculates the average of a player's batting by dividing the number of hits by the amount of times he batted and multiplying by 1,000.
Batting average A baseball player’s batting average is determined by dividing the number of hits by the number of times at bat and multiplying by 1000. (Batting averages are usually, but not necessarily, rounded to the nearest whole number.) For instance, if a player gets 2 hits in 5 times at bat, his batting average is
400
:
(
2
5
×
1000
=
400
)
. Partway through the season, a player thinks to himself, “If I get a hit in my next time at bat, my average will go up to 250; if I don’t get a hit, it will drop to 187.5.” How many times has this player batted, how many hits has he had, and what is his current batting average?
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1. The CLT provides an approximate sampling distribution for the arithmetic average Ỹ of a
random sample Y₁, . . ., Yn f(y). The parameters of the approximate sampling distribution
depend on the mean and variance of the underlying random variables (i.e., the population
mean and variance). The approximation can be written to emphasize this, using the expec-
tation and variance of one of the random variables in the sample instead of the parameters
μ, 02:
YNEY,
· (1
(EY,, varyi
n
For the following population distributions f, write the approximate distribution of the sample
mean.
(a) Exponential with rate ẞ: f(y) = ß exp{−ßy}
1
(b) Chi-square with degrees of freedom: f(y) = ( 4 ) 2 y = exp { — ½/ }
г(
(c) Poisson with rate λ: P(Y = y) = exp(-\}
>
y!
y²
2. Let Y₁,……., Y be a random sample with common mean μ and common variance σ². Use the
CLT to write an expression approximating the CDF P(Ỹ ≤ x) in terms of µ, σ² and n, and
the standard normal CDF Fz(·).
3. We'd like to know the first time when the population reaches 7000 people. First, graph the
function from part (a) on your calculator or Desmos. In the same window, graph the line y =
7000. Notice that you will need to adjust your window so that you can see values as big as
7000! Investigate the intersection of the two graphs. (This video shows you how to find the
intersection on your calculator, or in Desmos just hover the cursor over the point.) At what
value t> 0 does the line intersect with your exponential function? Round your answer to two
decimal places. (You don't need to show work for this part.) (2 points)
Chapter 2 Solutions
MyLab Math plus Pearson eText -- Standalone Access Card -- for Finite Mathematics & Its Applications (12th Edition)
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