Part 1
In the probability distribution to the right, the randomvariable X represents the number of hits a baseball player obtainedin a game over the course of a season. Complete parts (a)through (f) below.
x
P(x)
0
0.1689
1
0.3368
2
0.2831
3
0.1504
4
0.0374
5
0.0234
Question content area bottom
Part 1
(a) Verify that this is a discrete probabilitydistribution.
This is a discrete probability distribution because
▼
at least one of the probabilities is
all of the probabilities are
between
enter your response here
and
enter your response here,
inclusive, and the
▼
mean
sum
product
of the probabilities is
enter your response here.
(Type whole numbers. Use ascending order.)
(b) Draw a graph of the probability distribution. Describe theshape of the distribution.
Graph the probability distribution. Choose the correct graphbelow.
A.
01234500.10.20.30.4Number of HitsProbability
The graph of a probability distribution has a horizontal x-axislabeled "Number of Hits" from 0 to 5 in intervals of 1 and avertical y-axis labeled "Probability" from 0 to 0.4 in intervals of0.05. Vertical line segments are centered on each of the horizontalaxis tick marks. The approximate heights of the vertical linesegments are as follows, with the horizontal coordinate listedfirst and the line height listed second: 0, 0.34; 1, 0.15; 2, 0.02;3, 0.17; 4, 0.28; 5, 0.04.
B.
01234500.10.20.30.4Number of HitsProbability
The graph of a probability distribution has a horizontal x-axislabeled "Number of Hits" from 0 to 5 in intervals of 1 and avertical y-axis labeled "Probability" from 0 to 0.4 in intervals of0.05. Vertical line segments are centered on each of the horizontalaxis tick marks. The approximate heights of the vertical linesegments are as follows, with the horizontal coordinate listedfirst and the line height listed second: 0, 0.02; 1, 0.04; 2, 0.15;3, 0.28; 4, 0.34; 5, 0.17.
C.
01234500.10.20.30.4Number of HitsProbability
The graph of a probability distribution has a horizontal x-axislabeled "Number of Hits" from 0 to 5 in intervals of 1 and avertical y-axis labeled "Probability" from 0 to 0.4 in intervals of0.05. Vertical line segments are centered on each of the horizontalaxis tick marks. The approximate heights of the vertical linesegments are as follows, with the horizontal coordinate listedfirst and the line height listed second: 0, 0.17; 1, 0.34; 2, 0.28;3, 0.15; 4, 0.04; 5, 0.02.
D.
01234500.10.20.30.4Number of HitsProbability
The graph of a probability distribution has a horizontal x-axislabeled "Number of Hits" from 0 to 5 in intervals of 1 and avertical y-axis labeled "Probability" from 0 to 0.4 in intervals of0.05. Vertical line segments are centered on each of the horizontalaxis tick marks. The approximate heights of the vertical linesegments are as follows, with the horizontal coordinate listedfirst and the line height listed second: 0, 0.15; 1, 0.04; 2, 0.02;3, 0.17; 4, 0.34; 5, 0.28.
Describe the shape of the distribution.
The distribution
is multimodal
has one mode
is uniform
is bimodal
is multimodal
and is
skewed right.
roughly symmetric.
skewed left.
skewed right.
(c) Compute and interpret the mean of the random variableX.
μx=enter your response here
hits
(Type an integer or a decimal. Do not round.)
Which of the following interpretations of the meanis correct?
A.
In any number of games, one would expect the mean numberof hits per game to be the mean of the random variable.
B.
Over the course of many games, one would expect the meannumber of hits per game to be the mean of the random variable.
C.
The observed number of hits per game will be equal to the meannumber of hits per game for most games.
D.
The observed number of hits per game will be less than the meannumber of hits per game for most games.
(d) Compute the standard deviation of the random variableX.
σx=enter your response here
hits
(Round to three decimal places as needed.)
(e) What is the probability that in a randomlyselected game, the player got 2 hits?
enter your response here
(Type an integer or a decimal. Do not round.)
(f) What is the probability that in a randomlyselected game, the player got more than 1 hit?
enter your response here
(Type an integer or a decimal. Do not round.)
- Ea Top Part 1 In The Probability Distribution To The Right The Random Variable X Represents The Number Of Hits A Baseb 1 (8.71 KiB) Viewed 74 times