Math  /  Data & Statistics

QuestionUse n=6n=6 and p=0.25p=0.25 to complete parts (a) through (d) below. \begin{tabular}{l|l|} \hline 1 & 0.3560 \\ \hline 2 & 0.2966 \\ \hline 3 & 0.1318 \\ \hline 4 & 0.0330 \\ \hline 5 & 0.0044 \\ \hline 6 & 0.0002 \\ \hline \end{tabular} (Round to four decimal places as needed.) (b) Compute the mean and standard deviation of the random variable using μX=[xP(x)]\mu_{X}=\sum[x \cdot P(x)] and σx=[x2P(x)]μx2\sigma_{x}=\sqrt{\sum\left[x^{2} \cdot P(x)\right]-\mu_{x}^{2}} μX=\mu_{X}= \square (Round to two decimal places as needed.) σX=\sigma_{X}= \square (Round to two decimal places as needed.) (c) Compute the mean and standard deviation, using μX=np\mu_{X}=n p and σX=np(1p)\sigma_{X}=\sqrt{n p(1-p)}. μX=\mu_{X}= \square (Round to two decimal places as needed.) σx=\sigma_{x}= \square (Round to two decimal places as needed.)

Studdy Solution
Calculate the standard deviation using the binomial formula:
σX=np(1p)=60.250.75\sigma_X = \sqrt{n \cdot p \cdot (1-p)} = \sqrt{6 \cdot 0.25 \cdot 0.75}
σX=1.1251.0607\sigma_X = \sqrt{1.125} \approx 1.0607
Round to two decimal places:
σX=1.06\sigma_X = 1.06
The calculated values are: μX=1.50,σX=1.06\mu_X = 1.50, \quad \sigma_X = 1.06

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