Question

In the probability distribution to the​ right, the random variable X represents the number of hits a baseball player obtained in a game over the course of a season. Complete parts​ (a) through​ (f) below. x ​P(x) 0 0.1685 1 0.3358 2 0.2828 3 0.1501 4 0.0374 5 0.0254 ​

(a) Verify that this is a discrete probability distribution. This is a discrete probability distribution because all of the probabilities are at least one of the probabilities is all of the probabilities are between 0 and 1​, ​inclusive, and the sum mean sum product of the probabilities is 1. ​(Type whole numbers. Use ascending​ order.)

​(b) Draw a graph of the probability distribution. Describe the shape of the distribution. Graph the probability distribution. Choose the correct graph below. A. 0 1 2 3 4 5 0 0.1 0.2 0.3 0.4 Number of Hits Probability The graph of a probability distribution has a horizontal x-axis labeled "Number of Hits" from 0 to 5 in intervals of 1 and a vertical y-axis labeled "Probability" from 0 to 0.4 in intervals of 0.05. Vertical line segments are centered on each of the horizontal axis tick marks. The approximate heights of the vertical line segments are as follows, with the horizontal coordinate listed first and the line height listed second: 0, 0.15; 1, 0.04; 2, 0.03; 3, 0.17; 4, 0.34; 5, 0.28. B. 0 1 2 3 4 5 0 0.1 0.2 0.3 0.4 Number of Hits Probability The graph of a probability distribution has a horizontal x-axis labeled "Number of Hits" from 0 to 5 in intervals of 1 and a vertical y-axis labeled "Probability" from 0 to 0.4 in intervals of 0.05. Vertical line segments are centered on each of the horizontal axis tick marks. The approximate heights of the vertical line segments are as follows, with the horizontal coordinate listed first and the line height listed second: 0, 0.34; 1, 0.15; 2, 0.03; 3, 0.17; 4, 0.28; 5, 0.04. C. 0 1 2 3 4 5 0 0.1 0.2 0.3 0.4 Number of Hits Probability The graph of a probability distribution has a horizontal x-axis labeled "Number of Hits" from 0 to 5 in intervals of 1 and a vertical y-axis labeled "Probability" from 0 to 0.4 in intervals of 0.05. Vertical line segments are centered on each of the horizontal axis tick marks. The approximate heights of the vertical line segments are as follows, with the horizontal coordinate listed first and the line height listed second: 0, 0.03; 1, 0.04; 2, 0.15; 3, 0.28; 4, 0.34; 5, 0.17. D. 0 1 2 3 4 5 0 0.1 0.2 0.3 0.4 Number of Hits Probability The graph of a probability distribution has a horizontal x-axis labeled "Number of Hits" from 0 to 5 in intervals of 1 and a vertical y-axis labeled "Probability" from 0 to 0.4 in intervals of 0.05. Vertical line segments are centered on each of the horizontal axis tick marks. The approximate heights of the vertical line segments are as follows, with the horizontal coordinate listed first and the line height listed second: 0, 0.17; 1, 0.34; 2, 0.28; 3, 0.15; 4, 0.04; 5, 0.03. Describe the shape of the distribution. The distribution has one mode has one mode is multimodal is uniform is bimodal and is skewed right. roughly symmetric. skewed right. skewed left.

​(c) Compute and interpret the mean of the random variable X. mu Subscript xequals 0.1666 hits ​(Type an integer or a decimal. Do not​ round.) Which of the following interpretations of the mean is​ correct? A. In any number of​ games, one would expect the mean number of hits per game to be the mean of the random variable. B. Over the course of many​ games, one would expect the mean number of hits per game to be the mean of the random variable. C. The observed number of hits per game will be less than the mean number of hits per game for most games. D. The observed number of hits per game will be equal to the mean number of hits per game for most games. ​

Need help with (c) through (f) please!

(d) Compute the standard deviation of the random variable X. sigma Subscript xequals nothing hits ​(Round to three decimal places as​ needed.)

​(e) What is the probability that in a randomly selected​ game, the player got 2​ hits? nothing ​(Type an integer or a decimal. Do not​ round.)

​(f) What is the probability that in a randomly selected​ game, the player got more than 1​ hit? nothing ​(Type an integer or a decimal. Do not​ round.)

Answer 1

​(c) Compute and interpret the mean of the random variable
Which of the following interpretations of the mean is​ correct?
B. Over the course of many​ games, one would expect the mean number of hits per game to be the mean of the random variable.
​
(d) Compute the standard deviation of the random variable X.

​(e) What is the probability that in a randomly selected​ game, the player got 2​ hits?

We can find from the probability distribution table

P(X=2) = 0.2828

​(f) What is the probability that in a randomly selected​ game, the player got more than 1​ hit?

More than 1 hit means he can 2, 3, 4, and 5.

P(X>1) = P(X=2)+P(X=3)+P(X=4)+P(X=5) = 0.2828 + 0.1501 + 0.0374 + 0.0254 = 0.4957