A ditributor of computer oftware want to obtain ome cutomer feedback concerning it newet package. Three thouand cutomer have purchaed the package. Aume that 600 of thee cutomer are diatified with the product. Twenty cutomer are randomly ampled and quetioned about the package. Let X denote the number of diatified cutomer ampled. (a) Find the denity for X. (b) Find E[X] and Var X. (c) Set up the calculation needed to find P[X ? 3]. (d) Ue the binomial table to approximate P[X ? 3]

Answers

Answer 1

(a) The distribution of X is binomial with parameters n = 20 and p = 600/3000 = 1/5 since we are randomly selecting 20 clients without replacement and interested in the proportion of happy consumers. Given below is the probability density function for this binomial distribution.

f(x) is equal to (n pick x) * p * x * (1-p) (n-x)

Where p and 1-p are the probability of success and failure, respectively, and n pick x is the binomial coefficient, which is equal to n!/(x! * (n-x)!).

(b) The formula for the anticipated value of X, or E[X], is

E[X] = np = 20 * (1/5) = 4

Var X, the variance of X, is defined as follows:

Var X = np(1-p) = 20*1/5*4/5=3.2

(c) The cumulative distribution function of the binomial distribution's formula can be used to get P[X >= 3]:

Sum(i=3 to n) f for P[X >= 3] (i)

Summarizing from I = 3 to 20 and substituting the values from the density function, we obtain:

Sum(i=3 to 20) = P[X >= 3] [(20 pick I (1/5)*i*4/5*(20-i)]

(d) We must determine the value of the cumulative distribution function at x = 3, which is equivalent to the likelihood of receiving three or fewer successes out of 20 trials, in order to approximate P[X >= 3] using the binomial table. By using n = 20 and p = 1/5 to calculate the value of the cumulative distribution function at x = 3 in the binomial table, it is possible to determine this probability. P[X >= 3]'s estimated value is 0.586.

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Answers

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Therefore the function has a vertical asymptote at a certain x-value, then the function is undefined at that value.

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.......................................................

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[tex]\huge\text{Hey there!}[/tex]

[tex]\large\textsf{3x = 9}[/tex]

[tex]\large\text{DIVIDE 3 to BOTH SIDES}[/tex]

[tex]\mathsf{\dfrac{3x}{3}=\dfrac{9}{3}}[/tex]

[tex]\large\text{CANCEL out: } \mathsf{\dfrac{3}{3}} \large\text{ because that gives you 1}[/tex]

[tex]\large\text{KEEP: } \mathsf{\dfrac{9}{3}}\large\text{ because that helps us solve for x }[/tex]

[tex]\large\text{New equation: x = } \dfrac{9}{3}[/tex]

[tex]\mathsf{\dfrac{9}{3} = \bf 3}[/tex]

[tex]\boxed{\boxed{\large\textsf{Therefore, your \underline{answer} is: \huge \bf x = 3 }}}\huge\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

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