Question

Question 18 The probability that you will win a game is p = 0.88. If you play the game 1488 times, what is the most likely number of wins? (Round answer to one decimal place.) Let X represent the number of games out of 1488) that you win. Find the standard deviation for the probability distribution of X. (Round answer to two decimal places.) 20 and the maximum usual value Use the range rule of thumb to find the minimum usual value u H + 20. (Round answers to one decimal place.) Minimum Usual Value - Maximum Usual Value - Submit Question

Answer 1

18

Let the probability that you will win the game be p = 0.88

And

number of times play the game is n = 1488

Most likely number of wins = (n) * (p)

= 1488 * 0.88

= 1309.4

Standard deviation = sqrt(n * p * (1 - p))

                                 = sqrt( 1488 * 0.88 * ( 1 – 0.88) )

                                  = 12.53

Minimum usual value = 1309.4 – 2 (12.53)

                                    = 1283.94

Maximum usual value = 1309.4 + 2 (12.53)

                                     = 1334.46

5

The following table shows the provided outputs of the discrete random variables, along with the corresponding probabilities:

X	p(X)
0	0.0824
1	0.2434
2	0.3775
3	0.1589
4	0.1378

Now, we need to multiply the corresponding X outcomes with the corresponding probabilities, in order to compute the population mean μ:

X	p(X)	X⋅p(X)
0	0.0824	0⋅0.0824=0
1	0.2434	11⋅0.2434=0.2434
2	0.3775	2⋅0.3775=0.755
3	0.1589	3⋅0.1589=0.4767
4	0.1378	4⋅0.1378=0.5512

Therefore, the population mean is calculated as follows:

$\begin{array}{ccl} \mu = \sum_{i=1}^{n} X_i p(X_i) \\ \\ = \displaystyle 0\cdot 0.0824+1\cdot 0.2434+2\cdot 0.3775+3\cdot 0.1589+4\cdot 0.1378 \\ \\ = \displaystyle 2.0263 \end{array}$

6

given =

Probability [ plant grow healthy] = 0.9

Proabablity [ plant does not grow healthy] = 1 - 0.9 = 0.1 = p

⊳ The population proportion of success is p = 0.10,

also, 1 - p = 1 - 0.10 = 0.9,

and the sample size is n= 9.

We need to compute Pr(X=4)

This implies that

$\Pr(X = 4) = \left( \begin{matrix} 9 \\ 4 \end{matrix}\right) 0.10^{ 4} \times 0.9^{ 9-4}$

=0.0074

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